United States       Office of        EPA 520/1-87-024-1
          Environmental Protection    Radiation Programs     December 1987
          Agency         Washington, D.C. 20460
          Radiation
v>EPA     Low-Level and NARM
          Radioactive Wastes

          Model Documentation
          PRESTO-EPA-POP   .

          Volume 1

          Methodology Manual

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40 CFR Part 193                                  EPA 520/1-87-024-1
Environmental Radiation Standards                (RAE 8706/1-1)
for Management and Land Disposal
of Low-Level Radioactive Wastes
    PRESTO-EPA-POP:   A Low-Level Radioactive Waste Environmental
                      Transport and Risk Assessment Code


                              Volume 1

                         METHODOLOGY MANUAL
                            Developed by

                            D. E. Fields
                             C.A. Little
                            Fidel Parraga
                             Vern Rogers
                             Cheng Hung
                           December  1987
                            Prepared for
                U.S.   Environmental  Protection Agency
                    Office of Radiation Programs
                        Washington,  DC 20460
                     Cheng Hung, Project Officer

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                                DISCLAIMER
     The report  was  prepared  as an account of  work  sponsored  by an agency
of the United States  Government.   Neither  the  United States Government nor
any agency thereof, nor any  of their employees, contractors, subcontractors,
or their employees, makes any warranty, express or implied, nor assumes any
legal liability  or responsibility  for  any  third  party's  use of the results
of such use of any information,  apparatus,  product  or process  disclosed in
this  report,  nor  represents  that  its  use  by such  third  party  would  not
infringe privately owned rights.

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                             PREFACE







     Tnis  two-volume  PRESTO-EPA-POP model  documentation  provides



the background  information on the mathematical modeling  used  to



generate the  basic  data  for  the  Environmental  Impact  Statement



( E I S ) which  is  used to support EPA's  rulemaking for generally



applicable environmental  standards  for  the management  and



disposal of  low-level  radioactive wastes  (Llw).   Volume  1  of  the



PRESTO-EPA-POP  documentation presents  the  theoretical  bases  of



the mathematical model and their  implemented computer  code for



the assessment  of  the  cumulative  population  health effects



(including fatal cancer  deaths and  serious genetic effects)  to



the general  population residing  in  th.e  downstream regional basin



of a LLW disposal  site.   The model  simulates the  leaching  of



radionuc1ides from  the waste matrix,  the  hydro logical,



hydrogeo1ogica1, ana  biological  transports,  the resultant  human



exposures, and  finally the assessment  of  the probable  health



effects for  the entire regional  water  basin  population.  Volume



2 of the PRESTO-EPA-POP  documentation  provides the information



on the structure of the  computer  code  and  how  it  is used in  the



health effects  assessments.








     The two  volumes  present enough model  detail  so that



interested persons may apply the  model,  using  appropriate  and



applicable input data, for assessing  the  cumulative population



health effects  from a  LLW disposal  site.

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                           TABLE  OF  CONTENTS


                                                                    Page



 LIST OF  FIGURES	    vii


 LIST OF  TABLES	    viii


 EXECUTIVE  SUMMARY  	     ix


 1      INTRODUCTION   	     1-1

       1.1   Description of  a Low-Level Waste Disposal Site  .  .  .     1-1
       1.2   Description of  Model	     1-7
       1.3   Outline  of Methodology Manual   	     1-12


 2      DISCUSSION OF  METHODOLOGY  	     2-1

       2.1   Environmental Transport  Pathways 	     2-1

            2.1.1  Transport Pathways  Involving Water   	     2-4
            2.1.2  Atmospheric Transport Sources and Pathways   .     2-24
            2.1.3  Food Chain Calculations	     2-34

       2.2   Dose and  Health Effect Calculations	     2-44

            2.2.1  DARTAB Calculations 	     2-44
            2.2.2  Estimation of  Basement Dose to Resident
                  Intruder	     2-49
            2.2.3  Accounting for Radioactive Decay Products  .  .     2-56

       2.3   Health Effects to Regional Basin Population   ....     2-57

            2.3.1  Calculations of Regional Basin Health  Effects     2-60
            2.3.2  Conversion Factors for Regional Basin  Health
                  Effects	     2-63


3      DEVELOPMENT OF PRESTO-EPA-POP CODE   	     3-1

       3.1   Structure and Information Flow	     3-1
       3.2   Subroutine Description 	     3-3


4     DESCRIPTION OF OUTPUT OF THE PRESTO-EPA-POP CODE   ....     4-1

      4.1  Replication of Input Data	    4-1
      4.2  Organization of Input Data	    4-1

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                           TABLE  OF  CONTENTS
                              (Continued)
                                                                    Page
       4.3  Radionuclide  Summary Tables   	
       4.4  INFIL  Input/Output  	
       4.5  Unit Response Calculations  	
       4.6  Annual Summary Tables for Specified Years   .  .  .
       4.7  Radionuclide  Concentration Tables   	
       4.8  Radionuclide  Exposure Tables  	
       4.9  DARTAB Control Information  	
       4.10 DARTAB Dose Tables  	
       4.11 DARTAB Fatal  Cancer Risk Tables  	
       4.12 Residual Radioactivity Released to the Basin and
           Health Effects 	
4-3
4-4
4-4
4-4
4-5
4-5
4-6
4-6
4-6

4-7
REFERENCES
                                                                   R-l
APPENDIX A - A MODEL TO SIMULATE INFILTRATION OF RAINWATER
             THROUGH THE COVER OF A RADIOACTIVE WASTE TRENCH
             UNDER SATURATED AND UNSATURATED CONDITIONS . .  ,
A-l
APPENDIX B - AN OPTIMUM GROUNDWATER TRANSPORT MODEL FOR
             APPLICATION TO THE ASSESSMENT OF HEALTH EFFECTS
             DUE TO LAND DISPOSAL OF RADIOACTIVE WASTES . . .
B-l
APPENDIX C - RADE MODEL:  A RADIOACTIVE ATMOSPHERIC DISPERSION
             AND EXPOSURE CODE  	
C-l
                                   VI

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                              LIST OF FIGURES






Figure No.                                                            Page






   1-1   Environmental Transport Pathways Used in PRESTO-EPA-POP .    1-4






   2-1   Hydro!ogic Environmental Transport Pathways 	    2-2



   2-2   Atmospheric Environmental  Transport Pathways  	    2-3



   2-3   Trench Cap Removal Function 	    2-11



   2-4   Regional Basin Health Effects Pathway 	    2-59






   3-1   PRESTO-EPA-POP Subroutine Structure 	    3-2
                                     Vll

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                              LIST OF TABLES


Table No.
                                                                      Page
   1-1   PRESTO-EPA Code Family  .................    1-2

   1-2   Radiological  Exposure Pathways for Selected Scenarios .  .    1-13
   2-1    Leaching  Options  Specified  by  LEAOPT   ..........    2-13

   2-2    Units  of  Exposure Factor, E-JJ,  and  Dose  Rate  Factor,
         DF-j -ji ,  for  Selected  Individual  Dose Rate Calculations  by
         DARTAB   .........................    2-46
   2-3    Units of Years Lost  Factor, YLj j-| , and Mortality  Risk
         Factor, RF-,- j-| , for Health Risk Calculations by DARTAB  .  .     2-50

   2-4    Results of Basement  and Infinite Plane Unit Dose  Rate
         Computations  ......................     2-55
                                   Vlll

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                             EXECUTIVE SUMMARY










     The  U.S.  Environmental  Protection  Agency  (EPA)  is  responsible  for



developing  a  generally  applicable  standard  for   the   land  disposal  of



low-level radioactive waste (LLW).  As an aid in developing the standard, a



family   of   computer  codes,   entitled   PRESTO-EPA-POP,   PRESTO-EPA-DEEP,



PRESTO-EPA-CPG, PRESTO-EPA-BRC and PATHRAE-EPA,  has  been developed under EPA



direction.  The PRESTO-EPA-POP code was the first code developed and served



as the  basis  for  the other codes in the PRESTO-EPA family.  PRESTO-EPA-POP



estimates potential  health  effects  to local  and regional  basin populations



from the  shallow  land disposal  of low-level  radioactive  waste under a wide



variety of hydrologic, geologic, climatic, site engineering, and waste form



conditions.    The  EPA  uses  the  PRESTO-EPA  code  family  to compare  the



potential health  impacts  of a broad number  of LLW disposal alternatives to



evaluate and support its decisions for the LLW standard.





     In developing  the LLW  standard,  EPA  initially  identified more  than 24



distinct types  of radioactive  waste in various waste  forms  and  containers



which  required disposal  by  one or  more  of  eight  alternative  disposal



methods within  the  United States.   Basic requirements for  the  PRESTO-EPA



code family included:  (1) use of existing release and pathway models where



possible  to  reduce  development  time  and  costs;  (2)   use  of  modular



subroutines  to allow the use of  improved or more appropriate submodels when



available or  needed;  (3)  ability to  rapidly  and economically  execute  the



code  for  several   thousand   scenarios  or  alternatives  as  necessary;



(4) flexibility to  analyze a  wide  range of  hydrologic,  climatic,  waste



type,  and  site  engineering  combinations;  (5) use  of  EPA's health  risk

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 calculational  methodology;  and (6) results which are reasonably  realistic,



 reliable,  and  verifiable.





      The  user  of  the  PRESTO-EPA-POP code, may, with appropriate input data,



 simulate   a  specific  waste  type   (e.g.,  LWR  decontamination  resins),  a



 specific  form  for  the  waste  (e.g.,  solidified in  cement),  and  special



 containers  (e.g.,  300 year high-integrity containers).    The  user may also



 simulate  special  site engineering  and waste emplacement  configurations such



 as  sanitary landfill,  use  of deeper  trenches,  or  installation  of trench



 caps  with either  natural or  special low  permeability obtained from use of



 clays  and  compaction.    Although  most  shallow LLW  disposal  facilities



 consist of many disposal trenches, the PRESTO-EPA-POP code  treats  all  LLW



 trenches  and their  wastes  as  a single,  representative,  combined trench and



 volume of  wastes.





     Water, principally  from precipitation, is the primary agent of release



 and  transport   of  radioactivity  from   LLW  disposed  in   shallow  trenches.



 Geology,  hydrology, and  climate  also  affect not  only the mode and  rate of



 release,  but   also  which  transport pathways  dominate,  and  the  rate  of



 transport.  Therefore,  the input  data  portion  of the  PRESTO-EPA-POP code



 and  the  release  and  transport  subroutines,   have  been  designed  with



 sufficient  flexibility   to   accommodate  varying hydrologic   and  climatic



 conditions, ranging from typical  conditions found in the humid southeastern



 United States  to the arid southwest, with  reasonable accuracy  and realism.





     The  PRESTO-EPA-POP  code  can   simulate  the  following typical  water-



 related release  and  transport phenomena.   Precipitation  falling  on  the



ground surface  above  the trench is  apportioned  between  infiltration  into



the trench through  the  trench cap, drainage away from the site by  surface

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 runoff, and evaporation into the atmosphere.   The user can specify the time



 and  percent  of  trench cap  failure,  and  the time  duration  of  container



 integrity.   Radionuclides released from the waste by  infiltrated  water  are



 transported away  from  a LLW  disposal  trench  primarily  by groundwater  or



 surface runoff.   The   amount  of groundcover,  length  and  steepness of  the



 slope,  etc.,  and  runoff percent  can  be specified  to  simulate erosion of  the



 surface  soil   and  the  trench   cap.    Radioactively contaminated   water



 exfiltrating  into the  subtrench  soil  zone may  ultimately enter an  aquifer.



 Radionuclides   that  reach  the  aquifer  will   be  transported  horizontally



 within  the  aquifer.  These  radionuclides will  generally be  transported at a



 slower   rate  than  the  ground   water  velocity   in   the   aquifer  due  to



 hydrological  and   geochemical  interaction  with the  solid  materials in the



 aquifer which  retards  nuclide migration.   Some of the radionuclides which



 enter the  aquifer may  eventually reach  irrigation or water supply  wells or



 surface streams,  and  thus  become  available  for   uptake by  the   local



 population.  Residual  radionuclides   in  the aquifer  which are not  consumed



 by  the  local population are assumed to undergo  further transport to a  large



 downgradient  population (referred to as  the  "basin"  population).   Health



 effects  to  the  basin population  are calculated for  a time period of up to



 10,000 years.





      The overflow  of contaminated water from  the trench  onto  the surface



 soil  is simulated when  conditions  suitable   for  overflow  occur.   Once



 overflow has occurred,  the  radionuclides are  transported  by surface runoff



 into  nearby  streams and  may  become  available  for  human  consumption via



 irrigation  or drinking water.  Residual  radionuclides in  the streams which



are not  consumed during  the  "local" 1,000 year  assessment are assumed to be



released to  the  regional basin within one year.
                                        XI

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      The  exposure  of  the  local  population to radionuclides transported  from



 LLW  sites by  the  atmospheric pathway is also  simulated.   The atmospheric



 transport calculations nominally assume that  the  local  population resides



 within  a single  22.5-degree  sector.   User  specified parameters  give the



 fraction  of  the year  that the wind blows in that sector.  A simple external



 model  not contained  in the  PRESTO-EPA codes  (see Appendix  C)  enables the



 user  to make downwind atmospheric concentration calculations which properly



 distributes  atmospheric contamination  to  population centers  throughout  a



 360 degree circle  around the  site.





      Radionuclides  remaining  on  the  soil  surface  by  trench  overflow,



 spillage  during disposal  operations, or erosion  of the  trench  cap,  may



 become  suspended  in   the  atmosphere  and  transported  downwind where  the



 nuclides  may  be  inhaled  or  deposited  on  vegetation and  soil.   When  the



 radioactivity  is deposited, the PRESTO-EPA-POP  code simulates both external



 exposure  to  humans and internal  exposure from the ingestion of contaminated



 crops, meat, and mil k.





      The PRESTO-EPA-POP code allows the user to  select  special human exposure



 scenarios such as  an  inadvertent  intruder residing on or  farming the site,



 as well as  routine migration  of radionuclides  from  the trench through the



 hydrologic and atmospheric environmental  pathways to  crops  and  drinking



water.  Normal  scenarios  assume that the population  resides  downstream of



the plume  of  contamination and ingests radiorvuclides from various hydrologic,



atmospheric,  and food  chain pathways.   Processes  considered  in calculating



individual or  population  exposure  include:    groundwater transport  under



saturated  or  partially saturated flow  conditions, surface  runoff,  trench



water  overflow and  seepage, geochemical exchange, trench cap erosion, stream




dilution,  and resuspension  and atmospheric dispersion of contaminated  soil.
                                      Xll

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      Average annual  concentrations  of each  radionuclide in  environmental
 media (e.g., well water  or  the  atmosphere)  over the assessment period are
 used to calculate  radionuclide  concentrations  in foodstuffs.   Information
 from foodstuffs  and  human  ingestion  and  breathing rates  are utilized to
 calculate  the annual  average intake of radionuclides per individual in the
 population by ingestion and inhalation.   These intake data are  used by the
 DARTAB  subroutine  to  estimate  dose  rates,   health  effects,  and  genetic
 effects.

      The  PRESTO-EPA-POP  code  calculates  doses,  fatal  health effects,  and
 serious  genetic  effects   for  individuals  and  local  populations over  the
 period  of  assessment,  using  a  lifetable  approach developed  by  EPA.   This
 approach assumes  that each person  in the  population is a member of a large
 population  cohort  that   is  exposed  to   constant,  averaged  radionuclide
 concentration  levels.  Each member  of the population  is  assumed to ingest
 regional    average      quantities of food (vegetables, beef, and milk)  and
 water.   It is assumed  these  foods  are  produced on contaminated fields  and
 spray irrigated with  contaminated  water.   Beef  and milk  cattle are  also
 assumed to drink contaminated water.

      As  previously  mentioned, the  PRESTO-EPA-POP  code  also  addresses  on,
 request, special  exposure and pathway scenarios  for  inadvertent intruders
 residing on or farming the site.  The inadvertent  resident intruder scenario
 assumes that an  intruder  unknowingly excavates a  basement  in the  disposal
 trench while building a residence.   The individual is externally exposed to
 the buried  radionuclides because  the walls  of the basement of the residence
 are  assumed  to  be surrounded  by trench material.   The  time of residency
during the assessment  period  when  the residence  is  first occupied  and  the
                                    xiii

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 composition  of  the initial trench  inventory  which  contributes to exposure



 are  specified by the user.





     Farming the  site  after loss of  institutional  control  is  also treated



 as  a separate  intrusion  scenario.   By  farming  the  site,  the  farmer is



 affected  by  the  transport processes previously described.   In contrast to



 an  off-site  population,  however, the  farmer  may  ingest  crops  whose  roots



 have penetrated  into  the radioactive waste in the  trench.   The water used



 by  the  farmer for  irrigation  and  drinking  normally would  contain  a much



 higher  concentration   of  radioactivity  than   water used  by  the  off-site



 population  because  the  water  is  taken  from  a  well,  stream,  or  pond



 immediately adjacent to  the disposal  trench.   Farming  activities  may also



 mechanically suspend contaminated soil  into the atmosphere.   The time when



 mechanical  suspension  of  the  surface  soil   is  initiated   by farming  is



 specified  by the   user.    The  impact  of  such   mechanical  suspension  is



 calculated for both the farmer and the downwind population.





     The  PRESTO-EPA-POP  code can  be used  to make  health effect assessments



 for up to 10,000 years following the end of the disposal operations for the



 regional  basin population.  These assessments  are made  in two  stages.  The



 first stage calculates the health effects to the  local  population for up to



 1000 years,  and  the  second stage  calculates the  health  effects to  the



 regional  basin  population  over   10,000  years, using  a  synthesized  model



 community in the basin.   If necessary, the local assessment period,  which



 is a more detailed  analysis, can  be extended  for  several  thousand years or



more, but with a  significant increase  in computer  time and costs.





     The  health   effects  to  the  basin  population   are   based   on  the



cumulative  residual   radionuclides  leaving   the  disposal   area  with  the
                                      XIV

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 surface  water  or  groundwater.   Residual  radioactivity  is calculated, taking



 into  account the time  required for the  radionuclides  to  flow through the



 aquifer  from the local  use point to the  basin  stream, by considering the



 amount of  contaminated  water consumed or used by the local community during



 the  period  for  local  impact   assessment  and  the  dilutions  to  the  basin



 stream  by contributions  from  surface runoff  and  stream  flow  coming  from



 upstream of  the basin use  point.  After 1,000 years, the local community is



 assumed  to be  incorporated in  the  regional  basin  community  and the uptake



 of radionuclides  takes  place at the regional basin.





     The end of LLW disposal  operations  at a site is the starting time for



 the assessments  made by the code.   The user specifies the  length  of  time



 for the  local   assessment  period, up to  1,000  years.   The  regional  basin



 assessment period is optionally set equal to the local  assessment period or



 the local  assessment period plus 9,000  years.   For the  local  assessment,



 subtotals  for  the releases to  surface  water,  well, and  atmosphere  may be



 calculated and printed  at  a number  of  user-specified  time  intervals  within



 the assessment  period.   EPA normally  determines releases every  100  years



 for a  standard 1,000 year run.   Health effects  for the local  population are



 averaged over the length of the entire local assessment period.





     The time  step  for  the PRESTO-EPA-POP code is  fixed  at one year  and



default,  parameters   in   the model  give   annual  averages.    The  maximum



concentration of  each   radionuclide and  the year  of  the maximum for  each



nuclide is printed out  for  the  concentrations  in the  atmosphere,  well,  and



stream.





    Other features  in  the  PRESTO-EPA-POP model  and code include:
                                       XV

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      •     The  radionuclide  inventory  modeled accounts for  radioactive
           decay  during disposal operations.

      •     The  leaching of radionucl ides from the  trench waste materials
           can  be delayed by containment  in  high integrity waste con-
           tainers  if  specified by the user.

      •     In-growth   of   radiological   daughter   products   is   not
           calculated  explicitly by  the  model,  but  can be estimated by
           considering  the daughters  in  the initial  trench inventory
           for  some nuclides.

      •     The  sorption  and desorption characteristics of each radio-
           nuclide in the waste, the  surface  soil, the  geologic disposal
           media,  and  the  underlying  aquifer  can  be calculated  by  a
           linear model characterized by  four distribution coefficients,
           or Kj values.

      •     Groundwater flow in the host soil  and disposal  medium may "be
           either saturated or partially saturated.

      •     The  hydrologic  transport  of  radionuclides  vertically  by
           trench water from the trench  bottom  to the aquifer and then
           horizontally   through   the   aquifer   is   modeled  as  one-
           dimensional  flow with a correction made for dispersion.

      •     Because  many  of the  submodels in  the  PRESTO-EPA-POP  code
           were initially  developed  for  other  types of assessments and
           have been  adapted  to estimate  health effects  from  shallow
           land disposal  of LLW, the code is  modular in design to allow
           submodels  or   subroutines  to  be  replaced  when  desired  or
           necessary.

      •     Annual  hydrologic,  climatic, and meteorologic data which are
           used  for a  site  can   be  based  on the annual  variations
           recorded  in  30-year  or  other  long-term  averages   from  a
           nearby weather station  and  normalized  for input into  the
           PRESTO-EPA-POP code.

      «     There are no significant changes assumed in farming practices,
           demographics,  water and foodstuffs  usage,  or  climate during
           the period of analysis.


      The PRESTO-EPA-POP code  uses  unit response,  bookkeeping, and scheduled

event types of submodels.  The  unit  response submodels calculate the annual

response for  a process.   For  example,  the  INFIL unit  response  submodel

calculates  the  annual  infiltration  through an  intact  trench  cap.    This

annual infiltration  is then apportioned  within  each year  by the bookkeeping
                                       XVI

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 submodels.     Other  unit   response   models  calculate  the   atmospheric



 radionuclide concentration  transported downwind  per  unit source  strength



 and the annual  average erosion of the  trench cap.





      Bookkeeping submodels  follow the results  of unit response  submodels



 and user-supplied control  options.  For example, the TRENCH submodel, which



 maintains  a water  balance in the trench,  calculates  the  maximum  level  of



 standing water  in the trench and  the water  volume annually leaving via the



 trench  bottom or overflow.   Scheduled  event submodels consider the events



 such as   cap  failure,  basement  construction,  the  failure  of  container



 integrity, and  initiation  of scheduled mechanical  suspension of dust.  The



 timing  for these events  is specified by the  user.





      The  Environmental  Protection Agency wishes  to   warn  potential  users



 that, like any  complex computer code,  the PRESTO-EPA codes can  be  misused.



 Misuse  could  consist of  using the code to examine a site where  one or more



 critical modeling assumptions are invalid,  or where values for  significant



 input parameters are chosen that  do not  accurately  reflect  variables such



 as   radionuclide  inventory,   site  meteorology,  surface  and  subsurface



 hydrology  and geology, and future  population  demographics.  Certain release



 and  transport scenarios, such  as major changes in  meteorology or mining of



 the  trench contents,  are  not considered in the  PRESTO-EPA-POP  model  and



 code.  Significant changes to the  existing code and the input data  would be



 required to consider such  scenarios.   The  PRESTO-EPA  codes  were developed



 to  assess  and  compare alternative methods  for  managing and  disposing  of



 LLW  at  generic  sites for general  scenarios.   The  codes were not developed



to analyze  specific sites.
                                      XVll

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                              1.    INTRODUCTION










      The U.S.  Environmental Protection Agency (EPA)  is developing a generally



 applicable environmental  standard  for the  disposal  of  low-level  radioactive



 waste (LLW) to  support the U.S.  Nuclear  Regulatory  Commission  (NRC), the



 U.S.  Department of Energy  (DOE) and  others  in developing a  national  radio-



 active waste  management  system.   As  an aid in  developing  the standard, a



 family  of   computer  codes   entitled   PRESTO-EPA-POP,  PRESTO-EPA-DEEP,



 PRESTO-EPA-CPG,   PRESTO-EPA-BRC  and  PATHRAE-EPA was  developed  under EPA



 direction.  The  EPA uses  the  PRESTO-EPA code family to estimate and compare



 the potential  health  impacts  of  a  broad number of LLW disposal  alternatives



 for evaluation and  support  of  the  LLW standard.  Table 1-1 provides a  brief



 description  of each of these EPA codes.   These  codes, and how  the EPA uses



 them,  have  been  described  in  detail (Gal84).   Information  on obtaining



 complete  documentation  and users'  manuals  for the  PRESTO-EPA  family  of



 codes  (EPA85a  through  EPA85i,  MeySl,  Mey84)  is available from the EPA.





      The  PRESTO-EPA-POP code (Prediction  of Radiation Effects from Shallow



 Trench  Operations -  EPA  - Population), which  is  the first  member  of the



 family of  PRESTO-EPA codes  and the subject  of this document, is designed to



 permit the EPA to compare the relative potential population health effects



 of  different  management  and  shallow   land  disposal   alternatives  for



 low-level radioactive waste.
1.1  DESCRIPTION OF A LOW-LEVEL WASTE DISPOSAL SITE





     The description  of  the  life cycle of  a  shallow land disposal  site is




useful  in explaining  the modeling approach.  Following  site  selection and






                                       1-1

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                                 TABLE 1-1

                          PRESTO-EPA CODE FAMILY
PRESTO-EPA CODE
                        Purpose
PRESTO-EPA-POP
PRESTO-EPA-DEEP
PRESTO-EPA-CPG
PRESTO-EPA-BRC
PATHRAE-EPA
 Estimates cumulative population health effects to local
 and regional basin populations from land disposal of LLW
 by shallow methods; long-term analyses are modeled
 (generally 10,000 years).

 Estimates cumulative population health effects to local
 and regional basin populations from land disposal of LLW
 by deep methods.

 Estimates maximum annual whole-body dose to a critical
 population group from land disposal of LLW by shallow or
 deep methods; dose in maximum year is determined

 Estimates cumulative population health effects to local
 and regional basin populations from less restrictive
 disposal of BRC wastes by sanitary landfill and
 incineration methods.

 Estimates annual whole-body doses to a critical
 population group from less restrictive disposal of BRC
wastes by sanitary landfill  and incineration methods.
                                     1-2

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 procurement, trenches  are dug  on the  site.    Waste  materials in  various



 types  of containers  ranging  from  plastic bags or cardboard boxes to  steel



 drums   are   added  to  each trench.    There  is  currently  no   standardized



 container for LLW disposal.  Once a trench  is filled,  or  at various stages



 of filling, the  trench  may be  backfilled  to  eliminate voids   and decrease



 the  potential  for  subsidence and  cracking  of the  trench cap.  Following



 backfilling, the  trench  is  covered  with  a cap  of soil  or  clay,  one to



 several   meters  thick,   mounded  above  grade  to  facilitate  runoff  of



 precipitation  and decrease infiltration.   To  minimize erosion in non-arid



 climates,  the cap is seeded with grass or cover crop  and  is maintained for



 a  number of years.   Although  not all burial operations are identical, most



 current  and  past  LLW  facilities  have  included  some  of  the  practices



 described.





     In  general,  hydrologic  transport  is the major process  by  which the



 general  public  may  become  exposed to  radioactivity from LLW  disposed in



 shallow  trenches.  Figure 1-1 is a schematic description of the routes that



 water, and  any transported  radionuclides, may follow from  a trench in a LLW



 disposal  site.    The  major source  of  water at  existing   sites and,  it is



 anticipated, at future sites is precipitation.  Precipitation at a site may



 infiltrate  the  soil  or trench  cap,  run off the  surface, or evaporate.



 Depending on  the  groundcover,  length  and  steepness of slopes,  and other



 factors, runoff may cause erosion of soil from the surface.





     Hydrologic transport of  radionuclides  from  a  LLW  burial  trench  may be



 by  the  groundwater   or  via  the  runoff.   Groundwater   or  precipitation



entering the trench may mix  with  the waste material and  become contaminated.



This contaminated water  may  either overflow  the  top of  the trench  or
                                       1-3

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             PRECIPITATION
                                         ATMOSPHERIC TRANSPORT
                         RESUSPENSION

                            I ,
             DEPOSITION
                                                                            DRINKING WATER
                                                                             ft IRRIGATION
TRENCH CONTAINING
 LOW-LEVEL WASTE
          TRANSPORT TO AQUIFER
          AT RETARDED VELOCITIES
STREAM
                                                                                  WELL
         AQUIFER
                         TRANSPORT THROUGH AQUIFER AT RETARDED VELOCITIES
           FIGURE  1-1.   ENVIRONMENTAL TRANSPORT PATHWAYS  USED  IN
                           PRESTO-EPA-POP.
                                             1-4

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 percolate  downward through the bottom  of  the trench to the subtrench soil



 zone  and  ultimately enter an  aquifer.   In most cases, particularly in the



 arid  southwestern United  States,  the  disposal  formation  and  much  of the



 geologic  formations overlying  the  aquifer  are only  partially saturated.



 Transport  velocities are  different  for saturated  and partially saturated



 flow  but  can  be  calculated.    The  water  in the aquifer  will   have  a



 characteristic  flow velocity  from  a  few meters  per  year to  hundreds  of



 meters  per year.   Radionuclides  that finally  reach the  aquifer generally



 will  be transported  at velocities much  lower than  the characteristic flow



 velocity  of  the  water  in  the aquifer.    This  "retardation"  is  due  to



 interaction  of  the radionuclides .with the  solid materials  in  the aquifer.



 Some  of the  radionuclides  in the  aquifer may eventually  reach  the water



 supplying  irrigation  or  drinking   wells  or  a  point where   the  aquifer



 communicates  with  surface  streams.   Water  infiltration from the aquifer is



 used  by the  local  population.   Residual  radionuclides  in  the aquifer which



 are  not  consumed  by the local  population are assumed to  undergo further



 transport  to  a  large downgradient  population  (referred to  as the "regional



 basin"  population).   Health effects  to the  regional  basin  population are



 calculated for a time period of up to 10,000 years.





     A trench dug  in material  of low  permeability  may eventually overflow



 if rainfall is high enough and if water infiltrating into the trench is not



 removed.   Once overflow  has  occurred,  the  radionuclides may be transported



 by runoff  to  nearby streams  and  become available for human consumption via



 irrigation or drinking,  or else released  to  the  regional  basin  through  a



 basin stream.





     Humans away  from  the burial site  may be  exposed  to  the  contaminated




water if  this water  is   used  for  irrigation  of food  crops or  drinking.






                                       1-5

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Humans may also  be  exposed to radionuclides transported  from LLW sites by



atmospheric  processes.    Radionuclides deposited  on  the  soil  surface by



trench overflow,  by  spillage  during  disposal  operations, or  by complete



erosion  of  the  trench  cap,  may   be suspended  in  the  atmosphere  and



transported downwind  where  they  may be inhaled or deposited  on the ground



and vegetation.   Deposited radioactivity may contaminate  crops,  meat, and



milk  and  enter the food  chain.   Deposition on the  soil   surface may also



result in external radioactive exposure to humans.





     Besides  the  transport pathways  represented in  Figure 1-1,  there are



several other methods by which humans  can  be  exposed  to  radioactivity from



a LLW disposal  site.  If  the  trench cap is eroded  away,  the wastes will be



more  accessible  to  environmental transport  processes.   After the  end of



institutional control  of the site,  an  intruder  could  reside on or farm the



site.   It  is likely  the  intruder would receive an external  exposure from



the buried radionuclides  if excavation occurred near the  trench.  Factors



such as the  length  of residency, length of time after burial, and initial



radionuclide  inventory would all  contribute  to the amount  of  exposure and



subsequent dose and  health effects.





     Farming  the site  may  also result in off-site exposures to radioactivity



by mechanically suspending  contaminated soil in the atmosphere.  In contrast



to an  off-site  population,  however, a  farmer  may  ingest  crops  grown over



the trench  where the nuclide uptake  by  roots will be higher, because nuclide



concentrations  in the  soil  will be higher.  Also, depending on when farming



started,  the  on-site irrigation  water  may  contain  higher  concentrations of



radioactivity than off-site  water.
                                      1-6

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1.2  DESCRIPTION OF MODEL





     The model has been designed to calculate the doses and health effects,



resulting  from the disposal  of low-level  radioactive  wastes, to  a  local



population  and to  the  population  in  a hypothetical  regional basin in which



the disposal  site  is  located.   The impacts on the local and regional  basin



populations  are  analyzed  for a period  of  up  to  1,000 years.   The regional



basin analysis can be  extended  at  the option  of the user for an additional



9,000  years,  with the  local   population  assumed  to  become  part of  the



regional basin population.





     Many  of the  submodels  included  in PRESTO-EPA-POP were  developed  for



other types  of assessments  and  have  been adapted for the estimation of the



environmental  transport  of  radioactive waste  and  ensuing health  effects



from LLW disposal.  Because of this, PRESTO-EPA-POP is modular in construc-



tion to allow for  different  versions  of the submodels or subroutines to be



substituted,  if desired.





     PRESTO-EPA-POP  first   simulates   the   environmental   transport   of



radionuclides  from the low-level  waste  trench  to the  environments  of  the



local  and  regional basin  populations.  Then the  code calculates  doses  and



health  effects using  the DARTAB  model for  the local  population, and  a



separate health effects accounting model for the regional  basin population.



The calculations   in  DARTAB  are  based  on  average   internal  intakes  and



average external  exposures.    Internal  intakes   are  due to  ingestion  of



contaminated foods and  water, and  inhalation of contaminated air.   External



exposures   are due  to  contaminated   air  and  contaminated  soil.    For  a



detailed account of the DARTAB  methodology,  see Section 2.3 of  the DARTAB



documentation report  (Be81).
                                      1-7

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      The health effects calculations for the regional  basin  population  are
 based on the  cumulative  amount  of  radionuclides  released  to the  regional
 basin through  a basin stream during the assessment period  for the  regional
 basin,   which  is  usually  10,000  years.    The  transport  portion  of  the
 regional  basin  submodel  provides  the  cumulative amount  of  radionuclides
 discharged  into the  downstream  basin.   The subsequent  health effects  are
 calculated   by using  precalculated healtheffect conversion factors for each
 radionuclide  and region.

      The population  health effect assessment  begins  immediately after  the
 closure  of  the disposal site.   The  radionucl ide  inventories of the wastes
 in  the trench are calculated  to account for  the  radioactive decay during
 the  operational  period.  The waste  is  assumed  to  be containerized so that
 the   leaching  of  radionuclides  from  the  waste  cannot begin  until   the
 container fails.  The length of the container integrity  is a user specified
 parameter; therefore, a zero time should be specified when the waste is  not
 physically  containerized  or no credit is given for container integrity.

      The code  was  developed to handle a wide  variety of hydrogeologic  and
 climatic situations.   It can also handle waste  leaching and the groundwater
 transport of nuclides under partially saturated as  well as saturated hydro-
 geologic conditions,  while  taking  into account nuclide  retardation due to
 hydrogeochemical processes.   The  code has features  to account for the decay
 of  the  leaching  process  resulting  from the  use  of waste  containers; a
 farming  scenario  which  simulates farming over  the trench  with  vegetation
 root  uptake  of radionucl ides  from  the  waste;  and reduction  in  the trench
 radionuclide inventory at  the  start  of simulation because  of  decay during
the operational period.
                                      1-8

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      The ingrowth of  radioactive  decay products is  not  calculated by  the



 model  to maintain simplicity  and  to  reduce computer time and expense.   In



 cases  where  the major  dose  contribution  is  from external  exposure  to  a



 short-lived  progeny  in  equilibrium with a  parent  radionuclide  present  in



 the trench  inventory, the  user may wish  to  include  the  progeny  in  the



 trench inventory by  a method described  at the  end of  Section  2.2.3.





      Operational  spillage is defined  as  radionucl ides spilled from  incoming



 waste  packages  and  remaining on  the ground  surface at the  close of disposal



 operations.   These  radionuclides  would subsequently be transported either



 by  the atmospheric  pathway to the local population or by  the surface water



 pathway  to the  nearby stream.





      The complex  physical and  chemical interaction  between the radionuclides



 and the  solid  geologic  media has  been grouped into a  single  factor,  the



 distribution  coefficient, viz., Kd.   Different Kd values  can  be used  for



 soil,  the mixture  of soil  and waste  material  in the  trench,  sub-trench



 soil,  and the aquifer.





     The  subsurface  transport  path  of radionuclides  is  assumed to  be



 vertical  from the trench  bottom to the aquifer and then horizontal through



 the  aquifer.   The flow in the vertical  strata can  be calculated  either as



 saturated or  unsaturated  flow,  depending  on the  relationship  between the



 rate of  exfiltration,  the degree of  saturation, and  the  properties of the



 geologic  media.   However, flow  in the  aquifer  is  assumed to be  saturated.



 The  transport  of radionuclides  in  the  aquifer is calculated  by  employing



 Hung's "optimum  groundwater  transport model" (Hu81).  The  model  also  uses



 Hung's correction factor  which was  designed  to  compensate for the dilution



effects of dispersion on the health effects  evaluation.
                                      1-9

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      Three  types  of submodels  are  used in the  PRESTO-EPA-POP  code:   unit



 response  submodels,  bookkeeping submodels, and  scheduled event submodels.



 The  unit  response submodels calculate the annual  response of  a give process.



 For  example,  the  submodel  INFIL calculates the annual infiltration through



 an  intact trench  cap.   This  annual  infiltration  is then apportioned among



 the  transport  processes by  the  bookkeeping submodels.  Other unit response



 models  calculate  the  annual  average atmospheric  dispersion coefficient and




 erosion from the trench cap.





      Bookkeeping  submodels  keep  track  of the  results  of  unit  response



 submodels  and  user-supplied  control  options.   For  example,   the  TRENCH



 submodel  maintains  a  water balance in the trench,  calculates  the level  of



 standing  water  in the trench, and the volume of water leaving the trench.





      Average concentrations of each radionuclide over the assessment period



 in environmental  media, such  as well water or the  atmosphere,  are used  to



 calculate   radionuclide   concentrations   in   foodstuffs.       Foodstuff



 concentrations and average human ingestion and breathing rates are utilized



 to calculate  the  annual average radionuclide  intake  per  individual  in  the



 local population  by  ingestion and  inhalation.  These  intake  data  are then



 used  to estimate dose rate and health effects.






      The  atmospheric  transport  calculations made  by the code  assume  that



 the   total   population   resides   within   the  same   22.5-degree   sector.



 User-specified parameters  give the  fraction of year that the  plume blows  in



that  sector.   Therefore,  each  member  of the  population, breathing  at  the



same  rate, will inhale the same  quantity of each  radionuclide.   An  external



code, RADE (EPA85i), allows the user to  replace the atmospheric dispersion



calculation made for a  22.5  degree sector by the  PRESTO-EPA-POP code  with
                                      1-10

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 an  externally calculated equivalent dispersion coefficient for a number of



 Population centers  in  a  360  degree  circle enclosing the disposal site.  The



 RADE computer code  is  briefly  described  in Appendix C.





     Each  person  in  the  local  population  is assumed  to  eat the  same



 quantities and  varieties  of  food, all grown on  the same fields, and obtains



 his  or  her drinking and  crop  irrigation water from  the same source.   This



 assumption  simplifies  the  calculations  and  is appropriate  because  of the



 large  uncertainties in   predicting  individual  mobility,  population  demo-



 graphy,  agricultural  practices, geologic and hydrologic changes that might



 occur during  the 1,000  year local  analysis period.   As  input parameters,



 the  user may  specify the  fraction of the drinking and irrigation water that



 is supplied by  the  contaminated well or  stream.





     Doses   and   health  effects   to   populations   are   calculated   by



 characterizing  the  population  center for each  site with a single geographic



 centroid  location  and  the  total  population.    In  calculating  the  health



 effects, the  population  age  distribution and size is held constant over the



 assessment period.





     Scenarios  resulting  in  radiological exposure from the buried waste may



 be modified by  changing  input  parameters.  These scenarios include:  normal



 disposal site  operations; spillage  of  wastes  during  disposal operations; a



 resident intruder  on the  site;  farming  of the site; and  an eroded  trench



 cap with subsequent atmospheric contamination via suspension of mixed waste



material and  soil.   By changing the site  description  parameters,  the user



may design other scenarios of  interest.  To satisfy the needs of EPA for an



assessment of the total impact of a disposal  facility, the code is designed



to make  calculations for combinations of all  reasonable  exposure  pathways
                                       1-11

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 for  a  given  scenario.  The exposure pathways for each of  four  scenarios  are

 listed  in Table 1-2.


     Additional assumptions in the model and features of  the code  follow:


     •    Annual  average  meteorology  for  the  site is  part  of  the
          required input data.

     •    All  members  of the  population  use  the  same  sources of
          drinking  and  irrigation  water  contaminated  from  trench
          seepage or overflow.

     •    The  population  age  distribution and  size  are held constant
          over the assessment period.

     •    The  user  can   specify  the  fraction  of  the  drinking   and
          irrigation water that  is supplied by  the  contaminated  well
          or stream.

     •    Doses and  health effects  to  populations  are calculated  from
          population   centers for  each  site  characterized by a single
          geographic   centroid    location   containing   the   total
          population.

     •    Exposure from  the  eroded trench occurs  when  the  trench  cap
          has become completely  removed  by either erosion  or mechanical
          means.   Thereafter,  the eroded trench scenario may provide
          for  suspension  and  atmospheric  transport of trench contents
          and  resulting  inhalation  by  an individual  or the specified
          population.

     •    An individual may be directly exposed to  trench contents  and
          thus receive an external dose.  The   population may receive
          an external dose from immersion in  the suspended plume.

     •    The  code  is structured  to consider  only  one  scenario   per
          computer run.  The scenario to be  simulated may be designed
          by the  input values a user  chooses  for  such  parameters as
          population size, location and distance to  well, percent  cap
          failure, resuspension  rate,  etc.
1.3  OUTLINE OF METHODOLOGY MANUAL


     Chapter 1 provides an introduction  to  and  basis for the PRESTO-EPA-POP

code.  The description  is  given  of a  shallow land  disposal  site for LLW and

the potential  pathways  by  which  radiation exposures  to humans  might occur.


                                      1-12

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                      TABLE 1-2

RADIOLOGICAL EXPOSURE PATHWAYS FOR SELECTED SCENARIOS
    Scenario
 Normal
 Farming
 Eroded Trench
    Local Population

Ingests off-site water
Ingests off-site foods
Inhales downwind air

Ingests on-site foods
Ingests off-site water
Inhales suspended material
  at geographic centroid
Direct exposure from plume
                           1-13

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     In  Chapter   2  a  detailed  discussion  is   found  of  the  methodology



employed in developing the quantitative models for evaluating environmental



transport  pathways  and  calculating the  radiation doses,  associated  risks



and  potential  health  effects  to  individuals   and  selected  populations.



Appendices A and  B provide background  information  in  support of the models



employed in the code.






     Chapter 3  provides a description of the structure of the PRESTO-EPA-POP



code and its subroutines.





     Chapter 4  provides  a detailed  description  of  the  output  data  as



produced by the PRESTO-EPA-POP code.






     The PRESTO-EPA-POP  Users  Manual  (EPA85b)  provides  detailed  information



and guidance in  the  use of the  code  together-with  sample problems and  a



source  listing  of  the  code.
                                     1-14

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                       2.   DISCUSSION OF METHODOLOGY










 2.1   ENVIRONMENTAL TRANSPORT PATHWAYS






      Pathways for  environmental  transport of  radionuclides  considered  by



 the  model  are shown  in Figures  2-1  and  2-2.    Pathways  of environmental



 transport of  radionuclides that  involve  water  (Figure  2-1)  include  both



 surface  water  and groundwater.   Water may  leave the  trench  through the



 bottom or  by overflowing.   The  user may also  choose to allow  the  soil



 surface to  be contaminated  initially by operational  spillage.  Radionuclides



 in  water  near the  soil  surface may  be transported to a surface water  body



 or may enter the  aquifer by deep seepage.  Contaminated  water may ultimately



 reach  the local  population  by  use of water from  either  a  well  or surface



 water.   The regional  basin population will be exposed to the radionuclides



 that  enter  the  regional   basin  stream from  the  surface  water  body and



 groundwater.   Surface water transport to the  basin use point is assumed to



 take  less  than   one  year,  while  the groundwater  transport  takes  a much



 longer  time,  depending  on the distance of travel from  the local  to the



 basin  use  points  and  the  distribution  coefficient  of  the  radionuclide.



 Radionucl ides  not  used  by  the  regional  basin  population  are  assumed to



 enter  the ocean which  acts  as a radionuclide sink.






     Atmospheric  pathways  for  radionuclide  transport  considered by  the



model  are illustrated  in  Figure  2-2.   Material  may  reach  the  atmosphere



from  the  site   soil  surface  contaminated  by  overflow  or  operational




spillage, or  by the denuded trench  following  possible erosion  of the total



cap  sometime  in   the future.    The   local  population  may  ultimately  be



impacted by inhalation of or immersion in the suspended materials downwind,
                                      2-1

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           SPILLAGE
1
s
OVERFLOW
f i
f
SOIL
>URFACE
LEAC
HING





TRENCH
LEAC
^
HING
\
VERTICAL
SOIL
COLUMN


          BASIN
       POPULATION
         OCEAN
          SINK
                       SEEPAGE
                               GROUNDWATER TRANSPORT
DRINKING    INGESTION   DRINKING


\
HUMANS


                                       RAE-102206
FIGURE 2-1.   HYDROLOGIC  ENVIRONMENTAL TRANSPORT PATHWAYS
                          2-2

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           SURFACE
        CONTAMINATION
                       ERODED
                       TRENCH
                        SUSPENSION
                           LL
                            AIR
                 INHALATION
                 IMMERSION
    HUMANS
(Local Population)
               DEPOSITION
IRRADIATION FROM GROUND
                        INGESTION
 CROPS
  AND
GROUND
                                                  RAE-102094
   FIGURE 2-2.  ATMOSPHERIC ENVIRONMENTAL TRANSPORT PATHWAYS.
                            2-3

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by ingestion  of  crops  contaminated following deposition  on  soil  or crops,



or  by  direct  irradiation  from  ground   surfaces.    The  impact  of  the



atmospheric pathway  on  the regional  basin  population is considered  to be



negligible because of  its  distance from the disposal  site  and, therefore,



no calculations are made for the atmospheric pathway.





     The  approach  of the  PRESTO-EPA-POP  code  to  calculating radionuclide



concentrations  in  the  pertinent  environmental  media  is described  in  the




following two sections.





2.1.1  Transport Pathways Involving Water





     At  many  sites,  water  is  the most  important  medium for  transport of



radionuclides  away  from  the  trench.   Whether  the  transport pathway  is



predominantly  by  groundwater  or  by  overland flow  of water,  an  important



quantity  is   the  amount  of water  entering the   trench  via  infiltration



through the trench cap.






     The   basic  model   for   simulating   the  annual   infiltration   of



precipitation  assumes  that it  occurs in  two  modes:   (1)  annual  average



infiltration  which  is  dependent  upon  the  inherent physical  properties  of



the trench cap  and  (2)  infiltration  through failed portions  of the trench



cap.   Annual  average infiltration depends  upon  soil  properties,  seasonal



and annual  temperatures, amounts of precipitation,  rates  of  evapotranspira-



tion, and  other  similar physical  parameters.  Infiltration through failed



portions of the trench  cap  increases  with  time from  zero at  the  beginning



as the  percent of trench  cap   failure  increases.    The  year  when  failure



begins,  the rate of failure, and the final  percent  of  failure  are  specified



by the user and determine the amount of infiltration  due  to  cap failure.
                                      2-4

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      Infiltration  Through  Trench Cap - The  basic  model  for simulating the



 annual  infiltration  through  the  trench  cap assumes a portion of the trench



 cap  will  fail  and  allow the precipitated water to  drain  into  the trench.



 The  fraction  of the  trench which fails is  assumed to vary with time.





      Due  to the distinct nature of  the  infiltration  mechanism  between the



 intact  portion  and  the failed  portion  of the  trench  cap,  the  annual



 infiltration  through the trench cap  is divided into separate components.





      On  the  intact  portions  of the  cap,  the normal infiltration  rate  is



 calculated  by the method developed  by  Hung  (Hu83b) which  is described  in



 Appendix  A.   For the failed portion  of the cap, the infiltration is the sum



 of  rainfall  plus irrigation.   Therefore,  the  volume  of  water entering the



 trench annually is calculated by





                        WT = AT[fc(Pa+Ia)+(l-fc)WaJ                   (2-1)





 where





      Wj   = volume of water entering trench in current year



      Ay   = area of trench (m^)



      fc   = fraction of trench cap that has failed  (unitless)



      Pa   = annual precipitation (m)



      Ia   = annual irrigation (m)



      Wa   = annual infiltration (m)





      The value of Wj is added to the standing trench water from  the earlier



year  to calculate the maximum depth of standing water in  the trench for the




current year.
                                      2-5

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     The component  of annual  infiltration through the  intact  portion  of  the


trench cap, Wa, is  estimated by employing the infiltration model  developed


by Hung (Hu83b, Appendix A).  The model simulates the  rate of  infiltration


by solving system equations which describe  the  dynamics of  overland  flow,


subsurface flow, and  atmospheric  dispersion  systems.   The basic  equations


employed in the model  are



                            Qo  =  liH^iH5/3                         (2.2)
                                                                      (2-3)
                   EO =
En  when P + — > En
 p          At    p


P + •?-  when ED > P + — > 0
   At        P      At

            u
0  when P + — =0
           At
                    Ks  when P - E0 + — > K<-
                                      At    s

                    P - E0 +  -  when Kc > P - En + — > 0
                            At        b        °  At
                        0  when P - En + £- = 0
                                     0  At
                                              max
  Ks  when Zg < Z,

  0   when Zg = Zmax
                         dt
= (qi  - q0 + qt)/wg
                                         (2-4)
                                        (2-5)
                                                                     (2-6)
                                                                     (2-7)
                                                                     (2-8)
                                    2-6

-------
'F   -  F  '
.tp    to*
                                    1 +
                                         0.66(Wp
                                                          -1
2-9
                          dZp/dt = -fqp + qt)/Wp                     (2-10)


                          qt = ) qo  when Zp > 0                     (2_n)
                                 0   when Zp = 0


                       and qp = -Max(  qL  ,  qv  )                   (2-12)


where


     Q0   = rate of overland  flow per unit  width of  trench  cover  (m^/m-hr)

     H    = average depth of  overland flow  over the  entire  trench cover  (m)

     L    = length of slope or half  of trench  width  (m)

     n    = Manning's coefficient of roughness

     a    = average inclination of the trench  cover  (m/m)

     P    = rate of precipitation (m/hr)

     EQ   = rate of evaporation from the  overland  flow  (m/hr)

     q0   = rate of percolation from the  overland  flow  system  (m/hr)

     Ep   = evaporation  potential  (m/hr)

     q-j    = flux of moisture  infiltrating into the trench (m/hr)

     q^   = flux of pellicular  water transported  in  the  liquid phase  (m/hr)

     Ks    = saturated  hydraulic conductivity of the  soil (m/hr)

     Zq    = deficit of gravity  water (m)

     Zmax  = maximum deficit of  gravity  water,  equivalent to the thickness
            of the  trench  cover (m)

     Wq    = component  of wetness  for the  gravity water under a fully
            saturated  condition,  numerically identical to the porosity
            for  the  gravity water  (unitless)

     qL    =  flux of  pellicular  water transported in  the  liquid phase  (m/hr)
                                     2-7

-------
     Wp   = component of wetness for the pellicular water under fully
            saturated condition and is numerically identical to the
            porosity for pellicular water (unitless)

     Zp   = deficit of the pellicular water (m)

     De   = hydraulic diffusivity at equivalent wetness (m2/hr)

     Ke   = hydraulic conductivity at equivalent wetness (m/hr)

     qv   = flux of moisture being transported in the vapor phase (m/hr)

     qt   = flux of moisture being transformed from gravity water to
            pellicular water (m/hr)

     qp   = flux of pellicular water (m/hr)


     The annual infiltration  through  the trench cap is then  calculated by

integrating the hourly infiltration over the entire year.


     Trench  Cap  Modifications  -  The  trench  cap  may  fail  by erosion  or

mechanical  disturbance.   In the case  of erosion,  the annual  thickness of

material removed from  the  trench  cap by sheet  erosion  is  calculated using

an adaption of the  universal soil  loss equation  (USLE)  (Wi65).


     The annual amount of erosion is  subtracted  from the cap  thickness for

the current year of simulation.   If  the remaining thickness  is  less  than

1 cm, the cap  is considered to be completely failed and fc is  set  to  1.0.

The USLE may be written as


                            1L = fRfKf!_fSfcfpfD                       (2-13)


where


     IL   =  yearly  sediment  loss from  surface  erosion (tons/ha)

     fR   =  rainfall  factor  (fR  unit or  10Q  m-tons-cm/ha)

     f|<   =  soil credibility factor  (tons/ha/fR-unit)

     f[_   =  slope-length  factor  (unitless)
                                      2-8

-------
      fs   - slope-steepness factor (unitless)



      fc   = cover factor (um'tless)



      fp   = erosion control practice factor (unitless)



      fD   = sediment delivery factor (unitless)





      The parameterization  scheme of  McEl roy  et  al.  (McE76)  was  used  to



 specify  site-specific  values  of the  factors  in  Equation  (2-13).    The



 rainfall  factor,  fR,  expresses  the  erosion  potential   of  average  annual



 rainfall  in  the  locality.    The  soil  credibility factor,  fK;  is  also



 tabulated by McEl roy et al.  as  a  function of  five soil characteristics:



 percent silt  plus very  fine sand;  percent  sand greater than 0.1 mm; organic



 matter content;  soil structure; and  permeability.  The factors,  f|_ and  f$,



 for  slope-length  and  steepness  account  for  the  fact  that  soil  loss  is



 affected  by both  length and degree of  slope.  The  PRESTO-EPA-POP  code usage



 of  USLE combines  both  factors  into  a  single  factor  that may be evaluated



 using  charts  in McElroy et  al.  The  factor, fc,  represents the  ratio  of  the



 amounts  of  soil  eroded  from  land  that  is  treated   under  a  specified



 condition  to that  eroded  from clean-tilled  fallow ground under the same



 slope  and rainfall  conditions.   The erosion control practice  factor,   fp,



 allows  for  reduced erosion  potential  by the effect of practices  that alter



 drainage  patterns  and   lower  runoff  rate and  intensity.   The sediment



 delivery  ratio,  fn.,  is  defined by McElroy et  al. as the fraction  of   the



 gross erosion that is delivered to a stream..  Units of I|_ are converted to



 (m/yr)  within the  code.  See  Chapter 4  for a description  of input units.





     The  second method  of  trench cap  failure  accounts  for the  possibility



of mechanical disturbance due to  human intrusion or some other  means which



might  completely   destroy  portions  of the cap.    This   phenomenon  can  be



termed a partial  failure, but in reality is a total failure of some part of
                                      2-9

-------
the cap.   The  code user may specify  some  rate of cap failure  as  shown in

Figure  2-3.    By  specifying  appropriate  values  for  the  (x,y)  pairs  in

Figure 2-3, the  user  may  selectively  remove the cap  from  a  portion  of the

trench area.   Mathematically this function  is represented by


                    0 if tNYR2


Even  though  PCT2  might  be  less  than  1.0  in  year  NYR2,  the  cap  may

ultimately fail  completely by virtue of erosion.   As  f^ changes, the amount

of water added to the trench annually also  changes.


     The amount of water leaving the trench annually  via  the  trench bottom

is calculated by

                                   (DW+L)ITAT
                              VB =   W   L T T                         (2-15)

and
                               DW =  VATWT                          (2-16)
where
     Vg   = volume of water  leaving  trench  bottom  annually  (

     D\fj   = depth of water in  trench during current year  (m)

     Ij   = permeability of material  below  the trench  (m/yr)

     Aj   = trench  area (m2)

     V^j   = volume  of  water in trench (m^)

     WT   = porosity of trench contents (unitless)

     L     = length  of  saturated zone  (m)
                                      2-10

-------
<|3

£°
Li. ^
Ojf
zee
Q>
•o
o

ro
     PCT1
        o
	i
 NYR1           NYR2

    TIME (Years)
                                               RAE-102^24
              FIGURE 2-3.  TRENCH  CAP REMOVAL FUNCTION.
                             2-11

-------
     Water will overflow the trench if the maximum  depth  of standing water



is  greater  than  the trench depth.   If this  is  the case,  the  overflow is




calculated by





                             V0 = (DW-DT)ATWT                        (2-17)






where





     VQ   = volume of water overflowing trench in a  year



     D^   = depth of water in trench (m)



     Dj   = trench depth (m)



     Aj   = trench area (m2)



     Wj   = porosity of trench material  (unitless)






     Water  in  the  trench  may  be  contaminated  by  contact  with the  waste



material.   The user must  choose one of five methods shown  in Table  2-1 to



calculate the concentration of radionucl ides  in  the  trench water.






     Options  1-4  are  combinations  of two  factors:   the amount  of  waste



material  contacted  by water  and  the  method  of  partitioning  contamination



between waste  and water.   In options  1 and 3, where the  waste  is  in total



contact  with  the trench  water,  it  is assumed  that  the  total  volume  of



wastes  in  the trench  is  wetted each  year  as water trickles  from  top to



bottom  in  the trench.   In  options  2 and  4, wherein   the  wastes  are  not



totally  immersed  in  trench water  during  the  entire   year,  the  submodel



(immersed fraction)  calculates the wetted fraction as the  ratio of  maximum



water  depth  to  trench  depth.    Leaching  options,  1   and 2,  utilize  a



distribution coefficient,  Kd, to estimate the radionuclide concentration cj




in the trench water  based  on chemical  exchange (Equation 2-18a)
                                      2-12

-------
                        TABLE 2-1

          LEACHING OPTIONS SPECIFIED BY LEAOPT
Option                Leach Calculation Method
  1          Total  contact, distribution coefficient
  2          Immersed fraction, distribution coefficient
  3          Total  contact, solubility
  4          Immersed fraction, solubility
  5          Release fraction
                           2-13

-------
                            TCON
                                         (Chemical Exchange Option)  (2-18a)
,T
              =  Mi n
                       SNCNV    ITfw
                               (Solubility  Option)         (2-18b;
                              DmaxATwT
and
         TCON =  Min [TINFL/PERMT, 1]

where
    TCON  = estimates the average annual  fraction of the time that the
            waste is in contact with the  trench water
    TINFL = annual  infiltration rate (m/y.r)
    PERMT = trench  hydraulic conductivity (m/yr)
    Cy    = concentration of radionuclide in  trench water (Ci/cm^)
    Iy    = amount  of nuclide in trench  (Ci)
    f|d    = fraction of total  waste contacted by  water (=1 for LEAOPT = 1;
            <1  for  LEAOPT =  2)
    Ay    = trench  area (m^)
    Dmax  = maximum depth of standing water  (m)
    Wj    = porosity within  trench  (unitless)
    DT    = trench  depth  (m)
    K,j2    = distribution  coefficient within waste for radionuclide (ml/g)
    Pw    = density of  waste material  (g/cm^)
    S      = elemental solubility (g/ml)
    M      = mass  of radionuclide (g/mole)
    Nc    = ratio (Ci/mole)
    Nv    = ratio (ml/m^)
                                     2-14

-------
     Leaching  options  3  and  4 use  a solubility  factor to  estimate  the



maximum   concentrations   of   radionuclides   in  the  trench   water.    The



solubility option  may  be  used when information concerning K
-------
transport is  retarded,  relative  to the movement of water,  by vertical  and

horizontal retardation factors, RV and RH> as explained below:


     The groundwater flow in the  vertical  reach  is  assumed  to be saturated

or partially saturated.  The degree  of  saturation  is  used  to calculate the

water velocity, Vv and the vertical  retardation  factor,  Ry.   The degree of

saturation, SSAT, is either read in as an input parameter,  or is calculated

from the equation


                  SSAT = RESAT  + (1-RESAT) /AJJ[NEk\0-25           (2-19a)
                                           \ PERMV  /


where


   RESAT  = residual  moisture content, expressed  in  a  fraction of total
            water content when  saturated (unitless)

   ATINFL = average exfiltration rate (m/yr)

   PERMV  = vertical  saturated  hydraulic conductivity  (m/yr)


     Equation (2-19a) is based on  approximate  expressions for the fraction

of saturation (Cla78, McW79).  The exponent, 0.25,  is  generally a function

of  soil  type,   but  has  been   assigned  a   conservative  fixed  value  for

simplicity.    The  residual  moisture content, RESAT,  is an input  parameter

that is generally identical to  the  input parameter Wp of the  INFIL submodel.

The parameter ATINFL is  the  average  trench exfiltration rate.   When  there

is no overflow of trench  water, the rate is  calculated  by the expression


               ATINFL =  [PCT2 (PPN+XIRR)+(2-PCT2) XINFL]0.5          (2-19b)


where


    PCT2  =  maximum fraction  of trench cap failure  (unitless)

    PPN   =  annual  precipitation  rate  (m/yr)


                                    2-16

-------
    XIRR  = annual irrigation rate (m/yr)

    XINFL = infiltration rate through the intact trench cap (m/yr)
            (calculated by the INFIL subroutine)


     Vertical  water velocity Vv (m/yr), and the vertical  retardation factor

Rv  (unitless) are calculated as follows:


                          Vv = ATINFL/(PORV-SSAT)                   (2-19c)

                       Rv = 1 + (BDENS-XKD3)/(PORV-SSAT)             (2-19d)


where


    BDENS = host formation bulk density (g/cm^)

    XKD3  = distribution coefficients for the host formation (ml/g)

    PORV  = subsurface porosity (unitless)


On the other hand, the horizontal  retardation factor, R^,  is calculated as


                        RH = 1 + (BDENS-XKD4)/PORA                 (2-19e)


where


     XKD4 = distribution coefficient of the aquifer (ml/g)

     PORA = aquifer porosity (unitless)


     Finally,  the vertical  horizontal  transit  time,  ty (yr), and  t^  (yr),

are calculated according to
                        tv =    L ,       tH =     l                   (2-20)
                                               VH
where
     DV   = distance from trench  to  aquifer  (m)

     DH   = length  of aquifer  flow from trench to well  (m)


                                    2-17

-------
     Vy   = vertical  water  velocity  (m/yr)

     VH   = water velocity  in  aquifer  (m/yr)


Retardation, RV and RH,  are as previously defined.


     The breakthrough time, which "is  the time required for  a  radionuclide

to  travel  from the  bottom  of the trench  to  the well, is  the sum  of  the

vertical and horizontal  transit times.   A second  horizontal  transit time is

also calculated by the model,  which  is  the  time  it  takes for a  radionuclide

to  migrate  in  the aquifer  from the well point  to  the point of  release to

the basin stream.  This  transit time is  calculated  using  the corresponding

horizontal  distance from the well  to the basin stream.


     The  transport  of   radionuclides   in   the   aquifer   is evaluated   by

employing Hung's groundwater transport  model  (Hu81,  Hu86,  Appendix B).   The

basic equations for the  model  as adopted from  Hung  are
                         Q = zQ0 (T-RL/V)  Exp(-Xt)                    (2-21)
                  oo

and           z = /0.5(RP/7rW3)1/2 Exp C-NdW-(PW/4R)(R/W-l)2] dW      (2_22

                  °                  Exp(-RNd)
                           Exp    -  P-
                                2   2  f      PV  J
                               c    /
                               Exp  (
where
     z    = a correction  factor to  compensate  for the dispersion effect

     R    = retardation  factor, RV  or RH
                                     2-18

-------
     P    = Peclet number, VyDy/d or

     W    = dimensionless time, yV/L

     Nj   = decay number, XL/V

     L    = flow length, Dy or DH (m)

     V    = water flow velocity, Vy or V^ (m/yr)

     t    = transit time, ty or t^ (yr)

     d    = dispersion coefficient (m^/yr)

          = radiological decay constant (yr~l)

     y    = dummy time variable (yr)

     Q    = rate of radionuclide transport  at  distance L from  the  source
            (Ci/yr)

     Q0   = rate of radionuclide released at the  source (Ci/yr)

     T    = time of simulation (yr)


     To calculate  the  radionuclide  concentration  at  the  well  point, the

rate of groundwater flow in the plume of contamination at  the  well  point  is

calculated by


                    WA = VAPADA[V^T~+ 2 " tan(a/2)DH]             (2-23a)


where


     WA   = the  rate of contaminated water available  for  removal  from well
            (m3/yr)

     VA   = groundwater  velocity  (m/yr)

     PA   =  porosity of  aquifer material  (unitless)

     DA   =  thickness  of the aquifer  (m)

     a     =  constant angle  of  spread  of  the contaminant  plume  in the
            aquifer  (radians)

     Ay   =  trench  area  (m2)

     D     =  trench  to  well  distance  (m)
                                     2-19

-------
     The angle  "a"  is  the  dispersion angle of a  contaminated  plume  in the

water in an  aquifer.   This dispersion angle may  be  empirically determined

(e.g.,  by   field  dispersion  tests  wherein the  angle  of  dispersion  is

determined   from  measurements  of  chemical,  conductivity,  or  radioactivity

tracers in  water from a series  of boreholes  downstream across  the plume) or

it may  be  estimated.   The use  of a dispersion  angle is  consistent  with

published  characterizations  of  the  horizontally  projected  profile  of  a

chemical contamination front  as  it moves  through  an  aquifer (Sy81).


     The radionuclide  concentration  in  the  well  water,  Cy   (Ci/m3),  is

calculated  by

                                       •
                                  CW = -2-                           (2-23b)
                                      wA


     The total  water demand,  Vy,  including  drinking  water,  cattle feed, and

crop irrigation, is  calculated  by


                  Vu = [3.9X107WIfILI+UwLH+1.5X104LA]Np              (2-24)


where



     Vu   = annual well  water demand in liters  (1/person yr)

3.9X107   = 4492 m2  irrigated per person  X  8760 hr/yr

     Wj   = irrigation rate per  unit area (1/m2 hr)

     fj;   = fraction of year when irrigating (unitless)

     UN  = individual  annual water consumption (1/person  yr)

     LH  = fraction of drinking  water obtained from  well  water
      4
1.5x10   = water  fed  to  cattle  consumed  by  humans  (I/person yr)

     LA  = fraction of cattle feed water obtained  from well water

     Np  = size  of  the  population (persons)

     Lj   = fraction of  irrigation water  obtained  from well  water


                                     2-20

-------
      If the calculated total water demand, Vy, exceeds the flow rate of the

 contaminated  plume,  W/\, the  concentration of radionucl ides  in  the pumped

 out water is  recalculated using the actual volume of pumping to correct for

 the dilution  effect from the non-contaminated groundwater.  Units of Vy are

 converted to  cubic meters within the code.



      The  calculated  concentrations  of   radionuclides  in well  water  are

 averaged over the  length of the simulation  and  used  by  the  food  chain and

 human  exposure parts of  the  code for the drinking water and  cattle  feed

 pathways.



      Trench  Overflow Transport  and  Stream  Contamination  - As  previously

 mentioned, water  will  overflow the trench onto  the soil  surface  when the

 maximum depth of standing water  is  greater than  the trench depth.   If  this

 occurs, radionuclides will be added to the surface inventory of radionuclides

 deposited by  initial operational  spillage.  The surface soil  will  then  have

 a component adsorbed by the soil  with concentration C$ (Ci/kg) and  a compo-

 nent  of contaminated water in the surface soil of C^ (Ci/m3).  The  material

 adsorbed by the soil will remain  in the  soil  and becomes a source  term for

 resuspension  and  atmospheric transport  (this  process   is  discussed  in

 Section 2.1.2).  The contaminated water in the surface soil is available to

 enter  nearby  surface water  bodies  via  overland  flow,  or  percolate down to

 the aquifer.



     Radionuclides dissolved in the soil  water may either be transported to

 the stream by overland flow  or to the  deep soil  layers by percolation.   The

 amount of  each  radionuclide  added  to  the  stream is  represented  by  the


 product of C^ the radionuclide  concentration  in the surface  soil water,

 and the annual volume of runoff from the  contaminated soil  surface, WSTREM.

              c
The value  of  GW for each  radionuclide is  calculated  by

                                   2-21

-------
                                                                      (2-25)
                                  KdlMS+MW2/Pa


where

     CM   =  radionuclide concentration in surface soil water  (Ci/m3)

     IS   =  amount of radionuclide on surface (Ci)

     Kdi  =  distribution coefficient for surface soil region  (ml/g)

     MS   =  mass of soil in contaminated region (kg)

     Myj2  =  mass of water in contaminated soil region (kg),

     Pa   =  density of water (1 g/cm3)

     103  =  conversion factors used for Kd(l ml/g = 1 m3/103  kg) and  for
             dw  (1 g/cm3 = 103 kg/m3).

Equation  2-25 is used to  compute  the concentration of radionucl ides  in the

surface soil interstitial water.

     The  radionuclide  concentration  in  the  contaminated  surface  soil

region, C$,  is calculated using

                              GS = 10-3CwKdl                          (2-26)


     The  contaminated  region  of  surface  soil  is  defined  by  the  user  in

terms  of  length,  S|_  (m),  width,  Syj  (m),  and   depth,  SQ  (m).    These

parameters allow the calculation of  soil  mass  (M$)  and the water mass (M^)

in the contaminated soil  region by

                   MS =  103PSSWSLSD,   MW = 103WSSWSLSD               (2-27)

where


     PS   =  soil  bulk density (g/cm3)

     W$   =  soil  porosity  (unitless)

     103   =  (cm3 kg/m3 g)  for soil  and (kg/m3) for water

                                     2-22

-------
     Water  falling on  the  contaminated soil  region  may either evaporate,



 run  off, or  infiltrate.   Of the  liquid,  a certain  fraction  of the total



 precipitation, fr, will enter the  stream annually-





     The amount of water that enters the stream from  runoff of the contami-



 nated  region  is given by





                             Ws =  frPSwSL                            (2-28)





 The amount of water that enters deep soil layers and eventually the aquifer



 is given by





                                WD = WaSwSL                          (2-29)





 where  Wa is the yearly  farmland infiltration parameter.





     The annual contribution of radionuclides from the contaminated surface



 soil region  to the stream,  R$,  is then the  product  of Ws  and  the radio-

                                                   5

 nuclide concentration   in the surface soil   water C^ (Equation 2-25).   The



 amount of each radionuclide annually entering the deep soil layers from the



 contaminated surface soil region is the product of WD and C^.   The concen-



 tration of radionuclides in the stream is the quotient of R$ and the annual



 flow rate of the stream.





     As with  water  removal  from the well,  the  amount of each radionuclide



 removed from the stream is conserved by using





            IP = [3.9 x 107 WjfjS! + UWSH + 1.5 x 104SA] Np  C*      (2-30)





where





     IP   = annual  amount of nuclide removed from stream (Ci)



     CR
          = radionuclide concentration in stream (Ci/m3\

      n

                                      2-23

-------
      Si    -  fraction of  irrigation  water  obtained  from  stream


      SH    =  fraction of  drinking water  obtained  from  stream


      S/\    =  fraction of  cattle  feed water obtained from stream


 Other parameters are the same as defined  in Equation  (2-24).



      If  Ip is larger than the annual  input of that  nuclide to the stream,  R$,


 then  the radionuclide concentration  in the stream is recalculated referencing


 the water  volume removed from the stream  rather  than  the stream flow  by


                                   R    RS
                                  Cu=—                            (2-31)

                                   w    vy



      Mean  concentrations of  each  radionuclide  in  well  water  and  stream


 water are calculated  for  the  appropriate number  of  simulation  years  by


 dividing  the sum  of the  annual  radionuclide concentrations   in  the well


 water and the stream water by the length  of the  simulation.



 2.1.2 Atmospheric Transport Sources and  Pathways



      For some sites, atmospheric transport of  radionuclides  may be a major


 transport mechanism.  Therefore, careful  consideration must be given  in the


 formulation of the atmospheric transport model.  Another factor  which  was


 considered  in  generating  PRESTO-EPA-POP  was  the  desire  to minimize  the


 amount and  complexity of  input data.    The  compromise solution  to  these


 conflicting considerations  was to employ  in the  code  a  simplified, compact


 algorithm  suitable  for  those  sites where the  population  is  concentrated


 into a single,  small  community,  and  to make provision in the input data set


to  allow the code  user to  enter an externally computed population average


value   for  the  air  concentration,  X,  to  source strength,  Q,  ratio.   An


externally  computed  X/Q ratio  should  be  used  for  complex  population
                                     2-24

-------
 distributions.   An example  of a code which  could  be used for determining



 X/Q  in  such  cases  is  AIRDOS-EPA  (Moo79).





      In  most cases,  the  uncertainties in the  computed atmospheric source



 strength  for  contaminated  areas  are  larger than the differences between the



 internally  computed  and  externally  determined  (using  a  code   such  as



 AIRDOS-EPA)  X/Q ratios.   Use  of an external  code  has several advantages,



 however,  the most salient  being that  explicit specification  of complex



 population distributions  and the site  wind  rose removes the possibility of



 the   code user making   errors   of  judgement  in  determining  population



 centroids.





      Internal Model  Capability and Formulation - The atmospheric transport



 portion  of  the  PRESTO-EPA-POP  code  will  be  discussed in two parts:  (a) a



 description  of  source  strength   computation  and (b)  a discussion  of  the



 calculation  of  atmospheric  concentration  at  the  residence  site  of  the



 specified at-risk  population.    For most applications,  PRESTO-EPA-POP  is



 expected  to  be  applied  to a  site of known population distribution, and the



 user  must input geographical  and meteorological  parameters characterizing



 the  population  site  and  its relationship to the low-level  waste  disposal



 area.   The  formulation  of atmospheric transport  discussed herein  is  not



 intended  to  automatically identify  regions  of high  risk;  rather, it  is



 formulated to calculate risk-related  parameters  for a  particular, identified



 site.





     Where population  health effects  are to be determined,  the  geometric



population  centroid   specified  by   the   user  is the  point   for  which  a



22.5-degree sector average ground level  air concentration  is determined.



Where the population  distribution subtends from the waste  disposal  area  an
                                      2-25

-------
angle significantly greater than 22.5 degrees, the user should run the code

separately  for  each  sub-population.     A   mean   yearly  value  for  the

sector-averaged atmospheric concentration is computed by PRESTO-EPA-POP and

is input to DARTAB for use in computing external  exposures.


     The  most   common   approach  used  for   estimating   the  atmospheric

concentration and deposition of material  downwind from its point of release

is the Gaussian plume atmospheric transport model (S168).   This approach is

versatile and  well documented.   We  have  chosen  to implement  a  Gaussian

plume transport code called DWNWND (FiSOa)  as a module, in subroutine form,

in the PRESTO-EPA-POP code.


     User inputs for the  atmospheric  transport simulation allow specifica-

tion of  a  surface  radionuclide  concentration  at the waste  disposal  site.

Parameters used here include the initial  surface radionuclide inventory and

the  chemical  exchange  coefficient   for  surface  soils.   The  portion  of

radionuclide  sorbed  onto  soil   particles  is  considered  available  for

transport.  A source strength is computed  based  either  on a  time-dependent

(monotonically  decreasing)  resuspension  factor  or  a  process-dependent

mechanical   suspension  variable.    The  given  LLW   site   is  described  by

meteorological  variables  including:


     FN   =  fraction of the year wind  blows toward  at-risk individuals

     H    =  source  height  (m)

     H|_   =  lid  height  (m)

     S    =  stability  class

     T(j   =  type of dispersion  formulation

     Hr   =  Hosker  roughness  parameter (m)  (about .01 of the  actual
            physical  roughness)

     u     =  wind velocity  (m/s)


                                      2-26

-------
     V(j   = deposition velocity  (m/s)



     Vg   = gravitational fall velocity (m/s)



     x    = distance from source to receptor (m)





     Source  Term  Characterization  -  The  release   rate  for  atmospheric



transport  is  termed the  source strength.   In PRESTO-EPA-POP,  the source



strength  is  directly  dependent  on the  surface  soil-sorbed  radionuclide



concentrations  from operational  spillage  and  trench  overflow,  CQ  (Ci/m2).



The  source strength is the arithmetic sum  of two parts:  that parameterized



by  a time-dependent resuspension factor,  Re,  (An75)  and that parameterized



by a resuspension rate, Rr, (He80).





     First,  the wind-driven  suspension  component  is  described.    If  the



time-dependent  resuspension factor is defined as





                          Re = ReiexP(Re2yT)+Re3                    (2-32)





where T is elapsed time (days) and Re has units of inverse meters, then the



atmospheric concentration above the site, C^, is given by






                                 CA = ReCG                           (2-33)





and                          CG = CS PS SD 1()3                      (2-33a)










     Using Anspaugh's values of IxlO"4, -0.15, and IxlO"9 for Rei, Re2> and



Re3,  respectively,   the   value   of  Re  calculated  as  above  is  probably



conservative for humid sites.   As additional data from humid  sites become



available, model users may wish  to update the  equation  used for computing




Re.
                                   2-27

-------
     The  value of  elapsed  time appearing  in  Equation  (2-32)  is computed



 from  the  start  of  the  simulation.   It  is,   therefore,  correct  for the



 initial  surface inventory, but not for incremental additions thereto,  which



 may occur  at  later times.  However, when later additions result from trench



 overflow,  they will  likely consist of dissolved  material  and  would likely



 act  as  surface  depositions  of  mobile  particul ates.    It  is,  therefore,



 assumed  that  a  steady-state  asymptotic value  of  Re  is  for most   sites



 appropriate for later additions to the surface inventory.





     The  user wishing to  specify  a time  independent  windblown  resuspension



 factor may do so  by setting the values of Rei  and Re2 to  zero.   When this



 is done,  determination of  windblown  suspension  of all  contributions to the



 surface  inventory  will   be  treated  identically,  regardless  of time  of



 occurrence.





     In the above expression, C/\ is the atmospheric concentration of radio-



 nuclide  immediately  above the  site at  a  height  of about 1  m (Shi76), for a



 site of  large upwind extent.   Large  upwind extent  may be  interpreted  as



 exceeding  the atmospheric build-up  length,  given by  u Hp/Vq, where  u  is



 wind  velocity in  m/s,  HQ  is  the mixing  height (=1  m) ,  and  Vg  is the



 gravitational  fall  velocity.   The  representative  site extent  used  in the



 PRESTO-EPA-POP  code is  the  square root  of the  site  area,  A   (which  is



 characterized  by  S|_S^),  and  a tentative  correction  fraction,   F.    The



 correction factor  is computed using the equation






                                                                     (2-34)
                                      uHD





     With the stipulation that  the  value used' for F may  not  exceed unity,



the source term component (Ci/s) for windblown  suspension  is given by
                                      2-28

-------
                              Qr =
                                              (2-35)
     The  second source  component results  from mechanical  disturbance  of

site  surface  soil.   Mechanical  disturbance  occurs  during a user-specified

interval.   Within this  interval, the  fraction  of  time  per year  that  the

disturbance  occurs  is  Fmecn.    The  source  term component  for  mechanical

disturbance is  parameterized by  the  resuspension rate,  Rr, having  units  of

inverse seconds, as


                            Qmech = CGARrFmech                       (2-36)

The net source  strength for the site is the sum of these components:


                              Q = Qr + Qmech                         (2~37)

     Transport  Formulation - The  PRESTO-EPA-POP  code  uses a Gau,ssian  plume

atmospheric transport  model,  which is  an  extension of an  equation of  the

form (S168)
 X =
                exp
 y2
2V
+exp
                                                        1 /z+H
(2-38)
     This equation describes  Gaussian  distribution,  where X represents  the

radionuclide  concentration,  Q  the  source  strength,  and H the  corrected

source release height to be discussed later.  Dispersion parameters,  oy  and

CTZ, are the standard  deviations  of  the  plume concentration in the horizontal

and vertical directions, respectively.   The aerosol is assumed  to be  trans-

ported  at   a  wind speed   (height-independent)  u  to  a   sampling  position

located at  surface elevation  z and  transverse  horizontal  distance  y  from

the  plume   center.    Mass  conservation within  the  plume  is  insured  by

assuming perfect reflection at the  ground surface.   This is accomplished by
                                    2-29

-------
the  use  of  an  image  source at an elevation -H, which leads to the presence
of  two terms within the braces,  and  to the factor  1/2.   A correction  for
plume  depletion  will  be discussed later.   Equation  (2-38) may be obtained
from any of  several reasonable conceptual transport and dispersion models.

     Atmospheric  transport  at  several  sites  of  possible  interest  to
individuals  evaluating  consequences of low-level  waste transport have also
been considered elsewhere.  These include Hanford, Washington (Fi81, Mi81),
Savannah River, South Carolina (FiSOb), and Brookhaven, New York (Si66).

     Implicit in Equation (2-38)  is the assumption that the plume centerline
height is the  same as  the  release  height H.  In practice, the plume may be
considered  to  originate  at some  height, H, with  respect  to the population
at  risk.   Some  situations,  such  as  the existence  of a  ridge  between the
disposal  site  and the  population centroid,  may  dictate  use of an effective
height greater than  H  (e.g.,  the ridge  height).    The  plume thus  has  an
effective height, Heff, at which the  plume  may  be  considered to originate.
This effective value  should  be used  instead of the  actual  stack height as
the  starting point of  Gaussian plume  calculations.   If  the particulates in
the  effluent  have an  average  gravitational fall  velocity,  Vg, the plume
centerline  will  tilt  downward  with   an  angle  from the  horizontal,  the
tangent  of  which is  Vg/u.   The elevation  of the  plume centerline  at a
distance  x downwind is then

                       H =  Heff - xVg/u   for    H >. 0                (2-39)

and  it  is this corrected value that is used to  compute the aerosol  concen-
tration at  a distant  point.
                                      2-30

-------
     Effects  of  a  Stable  Air  Layer  on  Transport  -  The Gaussian  plume

formulation has been modified  for  use  in  PRESTO-EPA-POP  to account for the

presence of a stable air layer at high altitudes.  Upward dispersion of the

plume  subsequent  to  release  is   eventually  restricted  when  the  plume

encounters an elevated stable air layer or lid at some height  HL.   Pasquill

has  summarized some  reasonable  approximations  to  the  modified  vertical

concentration  profile   for  various  ranges  downwind  which are  used  here

(Pa76).  The limiting value of az may be defined  as


                        <7z(1imit) = 2(HL - H)/2.15                   (2-40)
                                           2


This  equation  follows  from setting the  ground-level  contribution to  the

plume from an  image source  located  above  the stable  air  layer to  one  tenth

the  value  of  the plume concentration.   It is  assumed  that  the  limiting

value of ffz calculated  in this  manner  is  correct for distances  beyond this

point.    For   shorter  downwind  distances  where  the  vertical  dispersion

coefficient O"z is less than crz(limit),  the Pasquill-Gifford value  ofaz is

used.  For greater downwind distances  where  o"z is  greater  than  or  equal  to

^(limit), the value of ^(limit) given in Equation (2-40)  is  used  instead.

The  lid height  is a  user-specified value  in the PRESTO-EPA-POP code.   For

LLW  applications, the  source  height  will   usually be  sufficiently  low

that  the  influence of  HL will  be small.   For  some  sites,  however,  the

influence of an intervening  ridge may necessitate a larger  effective source

height.


     Effects  of Plume  Depletion  -  The plume  is depleted  at ground  level

during  travel   as the  particulates   are  deposited.    Both   fallout  and

electrochemical deposition  may  be  important  considerations,  and  ground
                                    2-31

-------
 cover  characteristics  are  of  major  importance.    Under  certain  obvious

 conditions,  washout  is  also of  importance,  but those  conditions  have not

 been included within this model.  Fallout is partially quantified in the Vg

 term defined earlier.   Near ground  level  the  deposition  process  is often

 characterized  by a  deposition  velocity  Vd  (Gif62,  Mu76a,  Mu76b).   The

 deposition rate W is defined by


                                 W = Vd X                            (2-41)


 Where


     X    =  radionuclide concentration in air (Ci/nr).


     The magnitude of the plume depletion within the downwind sector may be

 found by  integrating  across  the plume.  Using  Equation  (2-38)  and  setting

 z = 0 it is  found that
£ • /"- M*
-co
— - — exp

- y2



H2"
- M Hy
2(7Z2
                      co         -~                -,                (2-42)
                  -co

     By  performing  the  indicated quadrature  across  the plume  and  further

integrating along the longitudinal  direction  to  express  the loss of  release

agent as a multiplicative factor, it can be  shown  (Mi78)  that the ratio of

the  air  concentration  considering  deposition  processes,  Xd,  to the  air

concentration without regarding  deposition, X, is
dx         (2-43)
                                f *L  /"-I exp  ["-
                                T u   J °z     L
                                    2-32

-------
 Since  (Tz  is  a complicated empirical function of x, Equation  (2-43) must be



 evaluated numerically.





      In the  PRESTO-EPA-POP applications, the average value of radionuclide



 concentration  X,  across  a  22.5-degree downwind  sector  is the  desired



 quantity.   In this  case,  the trans-sector  integration  leads to the value



 2.032  in  the air  concentration  equation (Cu76).   This  value includes the



 1/27T  factor  in Equation  (2-38).





      In conclusion,  assuming  that the radionuclide distribution  is  that of



 a Gaussian plume, we may compute  the mean radionuclide concentration, X, at



 ground level  for the 22.5-degree  downwind sector by
                         x = 2.032FdFwQ
                                uxO".
                                        exp
                                   z
 H'
20 2
                       (2-44)
                                                z
     The value of  H  in  Equation (2-44)  must be an effective source height.



This value  is corrected  in PRESTO-EPA-POP  for  plume tilt as  in  Equation



(2-39) and the accompanying discussion.   For use in the PRESTO-EPA-POP code,



H is on the order of 1 m for reasonably flat sites, but in many cases other



values should be used to  account  for local  site  characteristics,  e.g., for



the presence of updrafts.





     It has been noted that the choice  of plume  dispersion parameter o"z is



a user option in the PRESTO-EPA-POP code.  Choice of appropriate parameter-



ization depends  on site  meteorology,  topography, and  release  conditions.



The DWNWND  code (FiSOa),  which has been  included  as part of PRESTO-EPA-POP,



includes  a  choice of eight  parameterization  schemes for plume dispersion and



a  choice  of six stability  classifications.   The most  often used dispersion



parameterization  scheme  for  the   Gaussian  plume  is  the  Pasquill-Gifford
                                    2-33

-------
model.   This  is  the  approach most appropriate for long-term LLW assessment



calculations.  Likewise,  unless site-specific meteorology dictates otherwise,



the D stability category, denoting a neutral atmosphere, should be used.





     Pasquill  (Pa61,  Pa74)  considered  ground level  emission tracer studies



and wind-direction fluctuation  data  and developed dispersion parameter!'za-



tions for  six  atmospheric  stability  classes  ranging  from A, most unstable,



through  F, most stable.  Pasquill's values are approximate for ground level



emissions  of  low  surface roughness (Vo77).  These values  were devised for



small source  distances  (<1  km).  The  so-called Pasquil1-Gifford  form of



this parameterization  (Hi62)  has been  tabulated  by  Culkowski  and Patterson



(Cu76),  and are used in this model.





2.1.3  Food Chain Calculations





     Mean  concentrations  of  radionuclides  in  air,  stream water,  and  well



water are  calculated  by  the equations  listed in  Sections  2.1.1  and 2.1.2.



This section  describes how radionucl ides in those and  other  environmental



media are  used to calculate  human  internal  exposure and  potential  health



effects.





     Radionuclides  in  water  may  impact  humans  by  internal   exposure,



directly from  use  of drinking water or indirectly from use  of  irrigation



water used  for crops.   Radionuclides  in air  may impact humans  by  either



external or  internal  radiological doses.   External  doses may  result  from



immersion in  a  plume of contaminated  air or by  exposure to  soil  surfaces



contaminated by deposition from  the plume.   Internal  doses  may result from



inhalation  of  contaminated  air  or ingestion of  food  products  contaminated
                                      2-34

-------
 by  deposition from the  plume.   Dose and  health  effects  calculations are

 made  by the  DARTAB  program  (Be81)  which  is  utilized as  a  subroutine in

 PRESTO-EPA-POP.     DARTAB  will   be  discussed   in   some  detail   later.

 Radionuclide  input to DARTAB consists of the constant  concentrations in air

 (person-Ci/m3),  constant  concentrations on  ground surface (person-Ci/m2) ,

 constant collective ingestion  rate (person-pCi/yr) and constant collective

 inhalation   rate   (person-pCi/yr) .     Calculation   of  each  of  these  by

 PRESTO-EPA-POP will be discussed next.


     Concentrations of radionucl ides  in  air which  affect the  population or

 an  individual  are  calculated  as  described  in Section 2.1.2.  It is assumed

 that the mean nuclide concentrations in air are  constant  during the total

 period of the  simulation, as required, for  input to DARTAB.


     Concentration of  each  radionucl ide on  the  ground surface, Qs(pCi/m2)

 is  calculated  using


                              Qs = CSP + CSPO                        (2-45)


 where
     Qs   = concentration of radionucl ide on the ground surface at the
            populated area of interest
     CSP  = radionucl ide concentration in the soil used for farming due to
            atmospheric deposition
     CSPO = radionuclide concentration in the soil used for farming due to
            irrigation (pCi/m2)


Appropriate unit conversions are made within the code.


     The  collective   inhalation  rate   is   calculated  by  multiplying  the

population   size  by  the    generic    individual    inhalation   rate   of

radionucl ides.


                                      2-35

-------
                               Qinh = Ua CA                           (2-46)


where
     Qinh = Ci

     Ua   = inhalation rate (m^/yr)

     "C)\   = mean ground level  radionuclide concentration at a point of
            interest (Ci/m^)


The  units  of  Q-jnn are converted  to person pCi/yr for  input  to the DARTAB

subroutine.


     The collective ingestion  rate is the input to DARTAB that  requires the

most calculations by PRESTO-EPA-POP.  Ingestion includes intake of drinking

water,  beef,  milk, and  crops.    Except  for drinking  water,  all  of these

media may be contaminated by either atmospheric processes or by irrigation.


     The atmospheric  deposition  rate  onto  food  surfaces  or  soil  that is

used in subsequent calculation of radionuclide content in the food chain is


                             d = 3.6X1015 (TAVd                       (2-47)


where


      d   = mean rate  of  radionuclide deposition onto ground or plant
            surfaces (pCi/m^ hr)

      CA  = mean ground level  radionuclide concentration at point of
            interest (Ci/m^)

3.6X1015  = sec-pCi/hr-Ci

      Vd  = deposition velocity  (m/sec)


     The  following equation  estimates the  concentration  ITV  of a  given

nuclide in  and on vegetation at the  deposited  location  (except for H-3 and

C-14):

                                      2-36

-------
                             Yv Xe
where Tv is measured in pCi/kg, d is defined as above, and
     R    = the fraction of deposited activity retained on crops (unitless)

     Xe   = effective removal rate constant for the radionucl i'de from crops
            (hr~l), where Xe = X+XW,   is the radioactive decay constant
            andXw is the removal rate constant for physical  loss by
            weatheri ng

     te   = the time period that crops are exposed to contamination during
            the growing season  (hr)

     Yv   = the agricultural productivity or yield [kg (wet weight)/m2]

     B    = the radionucl ide concentration factor for uptake from soil by
            edible parts of crops,  [pCi/kg (dry weight) per pCi/kg dry soil ]
     CSP  = soil radionuclide concentration updated yearly

     P    = the effective surface density for topsoil [kg(dry soil)/m2]

     tn   = time interval between harvest and consumption of the food (hr)


                      CSP = (CSPL+dAt)exp[At(-X-X s)]


where


     CSP  = soil radionuclide concentration for this year

     CSPL = soil radionuclide concentration for last year
                                                       «
     d    = mean rate of radionuclide deposition

      X   = radioactive decay constant (yr~l)

     Xs   = rate constant for contaminant removal

     At   = time increment, equal to one year in PRESTO model


If  farming  is  performed  on  the trench  site,  then the  soil  radionuclide

concentration  is calculated as


                      SOCON =
                                      2-37

-------
 where


     SOCON  =  soil  radionuclide  concentration  (pCi/m2)

     SD     =  depth  of  contaminated  surface  region  (m)

     C$     =  radionuclide concentration in interstitial water of contaminated
             surface region  (Ci/m3)

     W$     =  porosity  of surface  soil  (unitless)

     C§     =  radionuclide concentration in  soil of  contaminated surface
             region  (Ci/kg)

     PS     =  bulk density of surface  soil (g/cm3)

     1012   =  pCi/Ci

     in3    = -kj- . cm^
             g    m3


 The  rate  constant  for contaminant removal  from  the soil, Rs,  is  estimated

 using
where


     Xs   = removal rate coefficient (hr~l)

     rs   = watershed infiltration (m/yr)

     PS   = soil bulk density (g/cm3)

     Kfj   = distribution coefficient (ml/g)

     Ws   = porosity (unitless)

     0.15 = depth of soil  layer (m)

     8760 = hr/yr


     Equation   (2-48)  is used  to  estimate  radionuclide  concentrations  in

produce  and  leafy  vegetables  consumed  by  humans  and  in  forage  (pasture

grass or stored feed)  consumed by dairy cows, beef cattle, or goats.


                                      2-38

-------
      The  concentration  of each radionucl ide in animal forage is calculated

by  use  of  the  equation


                           cf  =fpfscp +  d-Vs)Cs                     (2-50)

where


      Cf    = the  radionuclide  concentration  in the animal's feed (pCi/kg)

      Cp    = the  radionuclide  concentration  on pasture grass (pCi/kg),
            calculated  using  Equation (2-48) with tn = 0

      Cs    = the  radionuclide  concentration  in stored feeds in pCi/kg,
            calculated  using  Equation (2-48) with t^ = 2160 hr or 90 days

      fp    = the  fraction  of the year that animals graze on pasture
            (unitless)

      fs    = the  fraction  of daily feed that is pasture grass when the
            animals graze  on  pasture (unitless)


The concentration of each  radionuclide in milk is estimated as


                           Cm  = FmCfQfexp(-Xtf)                      (2-51)


where


      Cm    = the  radionuclide concentration per liter in milk (pCi/1)

      Cf    = the  radionuclide concentration in the animal's feed  (pCi/kg)

      Fm    = the  average fraction of the animal's daily intake of a given
            radionuclide which appears in each liter of milk (d/1)

     Qf    = the  amount of feed consumed by the animal  per day (wet kg/d)

     tf    = the  average transport time of the activity from the  feed into
            the milk and to the receptor (hr)

      X   = the  radiological  decay constant (hr~l)


     The  radionuclide  concentration  in meat  from atmospheric  deposition

depends, as with milk,  on  the amount  of  feed  consumed  and its  level  of

contamination.   The radionuclide concentration in meat is estimated using
                                      2-39

-------
                            CF  =  FfCfQfexp(-Xts)                       (2-52)


 where


      Cp   =  the  nuclide  concentration  in  animal  flesh  (pCi/kg)

      Ff   =  the  fraction  of the  animal's  daily intake  of  a  given  radio-
             nuclide which  appears  in each  kilogram  of  flesh  (d/kg)

      Cf   =  the  concentration  of radionuclide in the animal's feed  (pCi/kg)

      Qf   =  the  amount of  feed consumed by the animal  per day (kg/d)

      ts   =  the  average time from  slaughter to consumption  (hr)


      Concentrations  of  radionuclides  in  foodstuffs  that  result from spray

 irrigation with  contaminated water are estimated using essentially the same

 equations  as  for  atmospheric  deposition  with  the  following  differences:

 the  concentration in vegetation, TTV is estimated using Equation (2-48), but

 a  different  value  of the  retention fraction, R,  is used.  For irrigation,

 the  second term  of  Equation  (2-48) is  modified  by a factor of fj, fraction

 of  the year  during  which  irrigation  occurs and  the te in the  exponent

 becomes  tw,  equivalent  to fj  in  hours.    For irrigation  calculations,  the

 deposition  rate, d, in  Equation   (2-48)   becomes  the  irrigation  rate,  Ir,

 expressed as


                                IP = Cw K!                           (2-53)


 where


      IP   = radionuclide  application rate  (pCi/m2 hr)

     Cw   = radionuclide  concentration  in  irrigation water (pCi/1)

     MI   = irrigation  rate (l/m2
The concentration  in water,  Cw,  is an  average of  well  and stream  water

weighted by the respective amounts  of each that are used.
                                      2-40

-------
     Another modification introduced for irrigation calculations is related

to the radionuclide concentration in milk and meat where animal's intake of

water was added to Equation (2-51) and (2-52), respectively.  This becomes
                       cm = Fm(CfVcw Qw)exp(-Xtf)                  (2-54)


                       CF = Ff(CfQf+Cw Qw)exp(-Xts)                  (2-55)


where


     Qw   = the amount of water consumed by the animal  each day (1/d)


     Once  radionuclide  concentrations  in  all  the  various foodstuffs  are

calculated, the annual ingestion rate for each radionuclide is estimated by


                     Qing = Qv + Qmilk + Qmeat + QW                  (2-56)


where the  variables  represent  individual  annual intakes of a  given  radio-

nuclide via total  ingestion,  Q-jng> ancl ingestion of vegetation,  Qv,  milk,

Qmilk' meat» Qmeat'  anc'  drinking water, Qw,  respectively,  in  pCi/yr.   The

annual intakes  via each type of food, Qv for instance,  are calculated  as


                              Qv = (CV+CV)  Uv                        (2-57)
where
     Qv   = annual  radionuclide intake from vegetation (pCi/yr)

     CY   = radionuclide concentration in vegetation from irrigation
            (pCi/kg)

     CY   = radionuclide concentration in vegetation from atmospheric
            deposition (pCi/kg)

     Uv   = individual  annual  intake of vegetation (kg/yr)
                                      2-41

-------
     To  satisfy  the  input  requirements  for  DARTAB, the  annual  individual

intakes  are multiplied  by  the  size of  the population  to calculate  the

collective ingestion  annually.


     As  mentioned  earlier,  Equations  (2-47) through  (2-55)  do  not  apply

directly to  calculations  of concentrations  of  H-3  or C-14 in  foodstuffs.

For  application  of tritium  in irrigation water,  it  is  assumed  that  the

concentration in all  vegetation Cv  is the same  as the tritium  concentration

in drinking water;  therefore


                                 Cv  = Cw                            (2-58)


where Cv and Cw  are  in pCi/kg  and  pCi/1,  respectively.   The  concentration

of H-3  in  animal's feed, Cf,  is therefore also equal to Cw.    Then,  from

Equations (2-54) and  (2-55), the concentration of tritium  in animal's  milk

and meat can be written as


                            Cm = FmCw(Qf+Qw)                         (2-59)


                            CF = FfCw(Qf+Qw)                         (2-60)


where


     Cm   =  concentration of tritium  in  milk  (pCi/1)

     Fm   =  fraction of  the  animal's  daily  intake of  H-3 that appears in
            each  liter  of milk  (days/1)

     Cw   =  H-3  concentration in animal  drinking water  (pCi/1)

     Qf   =  animal's daily intake of  forage (kg/d)

     Qw   =  cow's daily  intake  of water  (1/d)

     Cp   =  concentration of tritium  in  animal meat  (pCi/kg)

     Ff   =  fraction of  the animal's  daily  intake of  H-3 that appears in
            each  kg of meat  (d/kg)
                                     2-42

-------
The  exponential  term is neglected due to  the  relatively  long  half life of

tritium as compared to transit times in the food chain.


     The root uptake of C-14 from irrigation water is considered negligible

and, therefore, has been set equal to zero.


     For vegetation  contaminated  by  atmospheric  deposition  of  tritium,  H-3

concentrations are calculated by


                        Cv = ^ (0.75)(0.5)(lxlOl5)                  (2-61)
                             h


where


     Cv   = H-3 concentration in vegetation (pCi/kg)

     C/\   = concentration of H-3 in air (Ci/m^)

     h    = absolute humidity of the atmosphere (g/m3)

     0.75 = ratio  of  H-3  concentration  in plant  water to  that  in
            atmospheric water

     0.5  = ratio of  H-3  concentration in  atmospheric water to  total
            H-3 concentration in atmosphere.

   IxlO15 - (lx!012pCi/Ci)x(103g/kg)


The  mean  ground  level  air  concentration   of H-3,  C^, is calculated using

equations in Section 2.1.2.


     For C-14, the concentration in  vegetation is  calculated assuming that

the  ratio of  C-14  to  be the natural carbon in  vegetation  is  the  same  as

that ratio  in the surrounding  atmosphere.  The  concentration of C-14  is

given by
                          Cv = CAT_ (O.il)(lxl015)                    (2-62)
                               0.16
                                    2-43

-------
where
     Cv   = C-14 concentration in vegetation (pCi/kg)

     C/\   = mean ground-level  concentration of C-14 in air (Ci/m3), also
            calculated from equations given in Section 2.1.2

     r    = ratio of the total release time of C-14 to the total annual
            time during which  photosynthesis occurs, r
-------
where  Kj  contains  any numerical  factors introduced by the units of E-jj(k),

the  exposure  to  the ith radionucl ide in the jth pathway, DF-jj] is the dose

rate factor of the  ith  radionuclide, the jth pathway and the 1th organ, and

P(k) is the exposed population  at  location k.   Note that all E-JJ and DF-jj]

for  various nuclides  (index  i) and organs  (index 1) have consistent units.



     DARTAB performs  three calculations and tabulations  for dose  rate and

dose:  (1) dose  rate  to an individual at a selected location, (2) dose rate

to  a mean or  average individual,  and  (3)  collective  population dose rate.

Table  2-2 lists units  of  DF-jj]  and  E-JJ for each  of  the  four pathways for

selected  individual dose calculations.  Dose rates, D-j ,-] , are in mrad/yr.



     Mean individual  dose  rates are  calculated using



                                 ? P(k) Dij^k)
                           D11.JL__
Note that in PRESTO-EPA-POP the impacted population is considered to reside

at only one  location  (k = 1).  Hence, calculations of mean individual dose

rate  are  numerically  equivalent  to  the  sum  of  pathway  doses  for  the

selected  individual  dose rate.   The  collective dose  rate for the exposed

population is the product of D-JJ] and the number of persons exposed.  Units

of the collective dose  rate are person rad/yr.



     The above dose rates may be expressed  in  a number  of different combina-

tions.  The doses can be summed directly over  pathways:



                           Dji(k) =  EDij^k)                       (2-65)
                                     j



or over all  nuclides:
                                       2-45

-------
                         TABLE 2-2

UNITS OF EXPOSURE FACTOR Eij, AND DOSE RATE FACTOR, DFi-p
 FOR SELECTED INDIVIDUAL DOSE RATE CALCULATIONS BY DARTAB
                                     Unit of Factor
        Pathway
Ingestion

Inhalation

Air Immersion

Ground Surface Exposure
       1j
                                                   DF
                                                     ij1
(person-pCi )/yr

(person-pCi )/yr

(person-pCi }/m?

(person-pCi )/m2
                                            (mrad/yr)/(pCi/yr )

                                            (mrad/yr)/(pd'/yr)

                                            (mrad/yr)/(pCi/m^)

                                            (mrad/yr)
                              2-46

-------
                           Djl(k) =  E DijTfk)                        (2-66)
                                     i
The total dose to the 1th organ at location k, D (k), is then


                          D!(k) = E  £  Di-pfk)                      (2-67)
                                  j  i


The dose equivalent  (mrem), H, for the 1th organ is given as


         H](k) = QF(iow-LET)Dl(low-LET)+QF(high-LET)Dl(k,high-LET)   (2-68)


where  QF denotes  the relative  biological  effect  factor.   The  factor is

defined  for each organ or health effect.


     To  combine dose  rates to different organs, a weighted sum is used


                           Dij(k) =  EVlTDi-pfk)                     (2-69)



where W] are  weighting factors  for the  various organ doses supplied by the

user where


                                 £ Wi = 1                            (2-70)
                                 1


Weighting factors  developed  by  EPA for  the  various  organs were  used as

input into DARTAB.   The International Commission on Radiological  Protection

(ICRP79) has proposed a similar approach to adding organ doses.


     Health  Effects Estimates - The  health effects  and  risk equivalent are

computed in  a manner  similar  to the  dose  calculations.   The health effects

or individual  risk  of premature death  to an  individual at  location  k for

the 1th cancer, ith radionuclide,  and jth exposure pathway is given by


                     Rijl(k)  = 10-5KjEij(k)RF1jl/P(k)                (2-71)


                                     2-47

-------
where  K-;  again serves  to reconcile the  units of  E-jj(k) and  RF-jj].   The

total  individual   risk  represented  by the  exposure  and  intakes  of  all

radionucl ides through all  pathways is given as


                R(k) - 10-5 £Kj £ Eij(k)  £ RFi-p/Pfk)               (2-72)
                            j    i        i


and  the health  effects  can  be  summed  over  pathways,  radionucl ides ,  or

cancers.   The mean  or  average individual risk  is  estimated  in  a similar

way.


     The  collective health  effects  are  expressed as  the  health  effects

rate.   For  example, the total  equilibrium fatal  cancer rate in an exposed

population is


                   HE =  ^^EKj  E  EE-j-U)!; RFi-M                 (2-73)
                         Te  j     k  1         1


where Te is the mean individual  lifetime  (70. 7y)



     In DARTAB, life loss  (years)  per premature death  is calculated by


                                ^Kj  f Eij(k)YLijl
                             =J-Aj - L_ - 1±L                   (2-74)
where
    YI(|<)  = average  life  lost  (years)  per premature death from cancer 1  at
            location  k

    YL-jji  = total  life  lost  (years)  for unit  exposure to nuclide i, pathway
            j,  and cancer 1

    ij(k)  = is  the exposure  to  or  intake rate of the ith radionuclide
            through the jth  exposure or intake mode at location k in the
            envi ronment
                                     2-48

-------
           = the mortality  risk factor per unit exposure or intake rate of
            the ith  radionuclide in the jth exposure or intake mode for the
            1th cancer site
      The  factor Kj  converts any  pathway specific  units  to  the required

units.   Note then that the  numerator  is  j.ust  the total  years of life lost

by  those  experiencing a cancer of  the  1th  organ, while the denominator is

the total number of deaths due to radiation induced cancers of the 1th organ.


      DARTAB  performs  two  calculations  and  tabulations of  life  loss  per

premature death (1)   life  loss  per  premature death for  an  individual  at a

selected  location  and  (2)  life  loss  per  premature  death  for  a mean  or

average individual.   Table 2-3 lists units  of  the exposure,  loss of life,

and risk mortality factors.


      The  mean   individual   life  loss per  premature death estimate,  Y],  is

merely  the   sum   over  all   locations,  k,  of   Y-|(k)  calculated   using

Equation  (2-74).   As with the  dose calculations, it should  be  noted  that

PRESTO-EPA-POP  assumes  that  the total  population  resides  at  one location,

k = 1.  Therefore, mean individual premature death values are equivalent to

those for the selected individual.


      Readers desiring a complete discussion of the development of the dose,

health effect,  or risk equivalent factors utilized by DARTAB should consult

the DARTAB documentation  report  (Be81,  pp. 5-10)  or  the supporting  report

(Du80).   The latter  describes  the theory  and  development of the  RADRISK

code that generates the risk factors utilized by DARTAB.


2.2.2  Estimation  of Basement Dose to Resident Intruder


     The DARTAB subroutine of the  PRESTO-EPA-POP  model  contains  algorithms

to compute the  dose  rate per unit  radionuclide  surface  concentration to an
                                      2-49

-------
                                   TABLE  2-3

     UNITS OF YEARS LOST  FACTOR,  Yl^-p, AND MORTALITY  RISK  FACTOR,
                    FOR HEALTH  RISK CALCULATIONS  BY  DARTAB
            (Corresponding  to Exposure Factors  Listed  in Table  2-2)
        Pathway
Ingestion

Inhalation

Air Immersion
                                             Unit of Factor
                                  YU
                                                             RFijl
                         yr  life loss/(pCi/yr)    (deaths/105 persons)/(pCi/yr)

                         yr  life loss/(pCi/yr)    (deaths/105 persons)/(pCi/yr)

                         yr  life loss/(pCi/m3)    (deaths/105 persons)/(pCi/m3)

Ground Surface  Exposure   yr  life loss/(pCi/m2)    (deaths/105 persons)/(pCi/m2)
                                       2-50

-------
"individual  standing  on   a  contaminated,  infinite  plane.    This  section

describes the calculation of a factor which is used to convert the input to

this  infinite  plane computation so  that  the  calculation computes  a  value

appropriate for an  individual spending  part of  his  time in  a basement.   In

this calculation it  is assumed  that  the basement  actually extends into  and

is surrounded by the trench contents.  Furthermore, it is assumed that most

of the  individual's  time  is spent at the  center  of  the basement, that  the

basement  radius  is  three  meters,   and   that  the  radiation  attenuation

coefficient  of  the  trench  may  be   approximated  by  that   of  soil, with

attenuation  coefficients  taken  from literature  published  by the  British

Standard  Institute  (BSI66).  The elapsed  time between  closure of the  waste

disposal  area  and  construction  of the  basement is an  input  parameter  for

the model .


     A conversion factor  F  is  defined which is used  to convert  the  radio-

nuclide  concentration  in  the trench surrounding  the  basement  to a  value

appropriate  for an  input  parameter to  the infinite plane  calculation.

Provided  the  basement  is  continuously occupied, this  conversion  factor  is

defined by the equation
                                 F = -—                            (2-75)
                                     Dp/A
where
          = dose rate in basement  per unit  of radionuclide concentration in
            trench [(mrad/yr)/(pCi/m3)]

     Dp/A = infinite plane dose rate per unit of surface concentration  on
            ground [(mrad/yr)/(pCi/m2)]
                                     2-51

-------
In  Equation  (2-75) A  represents the  radionuclide concentration  per unit

surface area on the infinite  plane and N represents the radionuclide concen-

tration per unit volume in the trench material.  If the value of the factor

F, is known the radionuclide  dose rate to  an individual within the basement

may be found by using  a modified form of the above equation


                            Db = _EL FN (mrad/yr)                     (2-76)
                                 A


     The  basement  whole  body gamma  dose  rate  per  unit  of  radionuclide

concentration at a distance one meter above  the  basement  floor is found by

integrating  the  radiation flux  from  each  volume  element  of the  trench

material  over the trench volume v


                   Db   =   C  B(/yT)exp[-(/ya^TrT)]dv              (2-77)
                   NC      -'y    r2


where


     C    = units transformation  constant  [(mrad/yr)/(pCi/m2)]

  B(AtTrt)  = build up factor,  using  formulas by  Eisenhauer  and Simmons
            for energies up to 200  kev  and Taylor's formula for
            energies above 200 kev.   Coefficients for  the  Eisenhauer
            and Simmons  equation  are  taken from Eisenhauer  and Simmons
            (Ei75)  and  for Taylor's  formula are taken  from  Morgan  and
            Turner  (Mor67)

     r    = distance from  point of  interest to  element  of  volume  of
            the trench  dv  (m)

    )U,a    = linear  attenuation coefficient of air (m"-'-)

    My    = linear  attenuation coefficient of trench  (m~l)

     ra    = distance in  air from  point  of  interest  to  element of  volume
            dv  (m)

     ry    = distance in  trench from  point  of  interest  to element  of
            volume  dv (m)

     v     = trench  volume  (m^)
                                     2-52

-------
      The  basement  may  be  considered  circular,  so  that  Equation  (2-77)

 becomes
                                             /y»
              B(/^jrj)   r  i LL   +i r \~\r\  +  I     D\' \f [/    r ILL   +f^-r  \ IH
       '(floor)     r2"       3              J v(waTT)    r2


           .R+d   ,,H+d
ir        I    r'.^V
  J      J
                                                                      (2-78)
          o       \\
          ^R+d     H
      27T/      /   r' B(^TrT)pxpr-fMara+/lTrT) IdZdr'
 where
      R     =  basement  radius  (m)

      h     =  distance  of  point  of  interest  from  floor  (h  =  1m)

      H     =  basement  height  (m)

      d     =  cut-off thickness  of  trench, chosen to  be  10 mean  free  paths
             (or
     The  first  integrand  refers  to  the section  of  the trench  immediately

 below  the  basement  floor, while  the  second  integrand refers to the  trench

 material  outside the  walls of  the   basement.   For  this  calculation,  the

 basement  is  assumed circular, and a  two-dimensional  Simpson's  rule  method

 (McC64) is used to numerically evaluate the integrals.


     Equation (2-78)  has been evaluated  to  determine  values  of the  ratio

 Ob/Me, and we have found that as  the assumed basement  radius varies from 3 to

 6 m, the completed value of D^/NC changes by only 30  percent  (being greater

 for the smaller basement radius)  for  radiation energies  ranging  from  20  keV

through 10 MeV.   Tabulated values of  the linear attenuation coefficient  for

air (Ko79) and for earth are used (BSI66).
                                      2-53

-------
     The dose  rate  at  a  height of one meter per unit surface concentration

 from an infinite plane is given by the equation
                          00
=  /   1- e"^ar ds = 27T  f 1
  J   r2               V  r
                                                    dr = 27TI         (2-79)
              AC
                                         1
 where


     C     = units transformations constant [(mrad/yr)/(pCi/m2)]
              oo
     I     =  f  0/r)exp(-Atar)dr (dimensionless)
            "1
     Aa    = linear attenuation coefficient of air (m~l)

     z     = height of point of interest (z = 1m)


     In  this  transformation,  the  incremental   area  element dS  is  27TXdX,

 where  X  is the  radius  projection  onto the  plane;  and since R2  =  X2 + 1,

 then have  XdX=RdR.   The  value  of  the integral, I, in this equation, may be

 computed numerically using  a polynomial  approximation  (Ga64)  for values of

Ma  corresponding  to different  values  of  gamma  energies.  The  results of

 these calculations are summarized in Table 2-4.


     The value of the ratio F as defined by Equation (2-75) may be obtained

 for a given energy by dividing  the results of the basement  calculation  by the

 results of the infinite  plane calculation.  Values of this  ratio for energies

 between  10 keV  and  10 MeV  are given  for a  basement  radius  of 3.0 m in

 Table 2-4.   A  very conservative average value of F may be chosen to be  0.1 m.


     If the basement  is occupied one-third of each day,  then the radionuclide

concentration  within  the  trench  is  one-third.   Therefore,  the basement

exposure dose  rate  in  the  infinite  plane  dose rate  calculation   of the

DARTAB  subroutine is found  by  multiplying  the  average  radionuclide  concen-
                                     2-54

-------
               TABLE 2-4

RESULTS OF BASEMENT AND INFINITE PLANE
      UNIT DOSE RATE COMPUTATIONS
          Energy
           MeV           F(m)

          0.05          0.015
          0.10          0.045
          0.20          0.061
          0.50          0.087
          1.0           0.087
          2.0           0.088
          4.0           0.092
          6.0           0.098
          8.0           0.099
         10.0           0.101
                   2-55

-------
tration  by the  volume  within  the  trench  during  the  basement  occupancy



period by  the  volume to the surface correction  term  F and the fraction of



time  the  basement  is  assumed to  be occupied.   Thus,  the  value of  A is



augmented  by the  quantity  0.033N to yield a  value  that corresponds  to the



plane dose plus the  basement dose.  In the computer code, the time at which



the  basement  is  constructed  is  a  user  input  parameter, and  the  average



radionuclide  concentration  by   volume  for  that  period  between  basement



construction  until   the  end  of  the  simulation  period  is computed  by the



code.    This  incremental  concentration is  added to  the  computed  average



surface  concentration  if the code  user  has elected  to include the basement



exposure mode.





2.2.3  Accounting for Radioactive Decay Products





     The code  does  not account  for ingrowth  of  radioactive  decay products



of materials during  storage in the trench  or  during environmental  transport



following  release from  the  trench.   The RADRISK  data files  accessed by



DARTAB do, however, include  dose  and  risk  factors that  account  for  such



ingrowth and  subsequent exposure  after  materials  have entered  the  human



body.  In  cases where the radioactive decay product is short-lived relative



to   the   parent,   the   radionuclide   concentrations    calculated  for  an



environmental  media may be in error because of this ingrowth.





     For example,  when cesium-137 (half-life  = 30 yr)  is included  in  trench



inventory,  barium-137m (half-life = 2.55 min)  should be in secular equilib-



rium with  the  parent  nuclide.   If  Ba-137m  is  not  listed as  part  of the



trench inventory,  then  no  environmental concentrations  will  be calculated.



Therefore,  external  exposures will  be underestimated because of the absence



of the  0.662  MeV barium-137m  gamma rays.   The  internal  exposures  will




include the exposure to these gamma rays as noted above.




                                     2-56

-------
      In  situations  where external  exposures may be important, the  user  may



 include  the  radioactive  decay  products  in  the  initial trench  inventory.   In



 such  cases,  the radioactive decay products should be entered with  the same



 activity,  decay coefficient, and environmental transport parameters as  the



 parent.    The  effect  of secular  equilibrium  will be  achieved throughout



 transport  in the environment.   The fact that  cesium and  barium probably do



 not  have identical   chemical and  environmental behavior will  be relatively



 unimportant  because of  the  short  half-life of the  progeny.   Entering  the



 decay product  in  the  source term  in  such  a   manner  will  not  grossly



 overestimate internal  exposures because the dynamics  of the  decay  products



 inside  a human body tend  to result in low doses.   In  particular,  this  is



 true  because the RADRISK  data base,  which contains risk  factors  used  by



 DARTAB,  will not be affected   by  the decay  rate  of  the  decay  product  as



 indicated  in the  environmental  transport  portion  of the input data set  (K.



 F. Eckerman, Oak Ridge National Laboratory, personal communication).









 2.3   HEALTH  EFFECTS  TO REGIONAL BASIN POPULATION





      The PRESTO-EPA-POP  model   evaluates  the   cumulative  health  effects   to



 the population  of a  regional basin  downstream from the  disposal  site for a



 period of 10,000 years after site closure.  Because of the uncertainties  in



 predicting  health  effects  over long periods  of  time,  and  to  reduce  the



 computer costs, the  analysis is divided in two parts,  the primary analysis



 and the  basin  analysis.   The  primary analysis, for 1000 years,  simulates



the health  effects   to  the  local  community as described in the  previous



sections.
                                      2-57

-------
     Those radionuclides not used or consumed by the local community during



the  first 1000  years  are  considered  to be  residual  radionuclides.    In



addition,  after  the  1000  year  local  assessment  period  has  ended,  all



radionuclides  that  leave the  disposal  site  and  enter the  regional  basin



(which  now incorporates the  local  area, see  Figure  2-4)  are considered



residual  radionuclides.  In the  regional  basin  analysis,  health effects to



a  regional  basin  population  are  calculated  for  10,000  years   for  all



residual  radionuclides entering the downstream regional basin, using health



effects conversion  factors.  The  total  health effects  are equal to the sum



of the  health  effects obtained from the  primary  analysis and the  regional



basin analysis (see Figure 2-4).





     The  regional  basin analysis  assumes  that  all   of the  communities



located  in a  regional  water   basin  downstream  from  the  disposal  site,



including the  community  analyzed  in the  primary analysis, can  be combined



into a single composite community.  The transport of radionuclides from the



disposal  site,  through  the  hydrologic pathway, continues  as described  for



the primary analysis.   The  atmospheric transport pathway  is not included,



since  it  is  assumed  that  the  health  effects to  a more  distant  regional



basin from this pathway will  be negligible.





     Instead   of  performing  lengthy   food chain   simulations  and  health



effects analyses  for  10,000 years,  the model  calculates  the impact on  the



basin based on the  "residual radionuclides" released  downstream.   Residual



radionuclides   are the sum  of  those  nuclides released  from the  LLW  site



which are not  used  by the  local community during the  primary analysis  and



the radionuclides  released  to  the  downstream basin  during  the  period  of



regional  basin  analysis.  The  radionuclides considered are those that enter
                                    2-58

-------
 YEARS 1 - 1,000
                     AQUIFER
                                               YEARS 1,001 - 10,000
                                LOCAL STREAM  S —  	
                                                           AQUFER
BASIN RESIDUAL RADIOACTIVITY:
        B(CO=CA-W) + (
REGIONAL BASW HEALTH EFFECTS:
            HE = BxHECF
                   - Y)
BASIN RESIDUAL RADIOACTIVITY:
       B(co  =  D + S
REGIONAL BASW HEALTH EFFECTS:
        HE = BxHECF
                                                         RAE-102208
FIGURE 2-4.   REGIONAL BASIN  HEALTH EFFECTS  PATHWAY.
                          2-59

-------
 the  aquifer through  the  trench  bottom  and those  that  enter the  regional



 stream  by way of  runoff.





      In order  to  determine  the  health  effects  to  the  regional   basin



 population,  the  residual  radionuclide activity  released to  the  regional



 basin is multiplied  by  a  conversion factor  Recalculated for  each   radio-



 nuclide within  PRESTO-EPA-POP code.       The conversion  factors, which are



 nuclide dependent,  are based  on local water  use  characteristics  and the



 hydro!ogic pathway.





 2.3.1   Calculations of Regional Basin Health Effects





     The code uses health effects conversion factors (see Section 2.3.2) to



 calculate the  health effects  to the  regional   basin  population from the



 basin residual  radionuclides.   The  basin  residual  radionuclides  consist of



 all the radionuclides that leave the disposal site area through the  surface



 and underground water pathways but are not used  by the local  population and



 go on to enter  a  major  basin stream.   Once the  radionuclides arrive at the



 basin stream,  they  are  released  to  the  basin  within   the  same year  of



 arrival.  Radionuclides  not  used by the regional  basin community are  assumed



 to travel to the ocean where they contribute no  health effects.





     Releases of  radionuclides  to the  regional  basin can  be  simulated for



 up to 10,000 years.  The  annual  nuclide releases  to the  regional  basin are



 collected in the  model  in  ten periods of  1,000 years  each.   The  annual



 releases of  each nuclide from surface runoff and the aquifer to the regional



 basin during the first millenium are collected in the array variable QDWSB.



Nuclides that leave the  bottom of the  trench during  the first millenium and



arrive  at  the   well  beyond  year 1000  are  not  neglected;  they  are  also



considered in the  yearly loop.






                                    2-60

-------
     In each of the first thousand years of simulation, the amount released



to  the  basin, SSTREM(N),  is decreased  by  the amount  of  nuclides removed



from the  nearby  stream(s) with  water  used by the  local  population.   This



correction  is  accomplished  using  the  stream  flow  rate,  STFLOW;  the



hypothetical  volume  of water  withdrawn  from  the  stream, VOLUSS;  and the



stream water concentration,  STCON(N).  The  nuclide  release to the basin in



each year of the first millenium is





          |(STFLOW - VOLUSS) STCON(N)  if VOLUSS < STFLOW            (2-80)



          I           0                if VOLUSS _> STFLOW





     To calculate radionuclide contributions from the aquifer to the basin,



it  is necessary  to  evaluate additional  radionuclide transit  times  as  well



as  Hung's  correction  factors  for  the reach  from the  well to  the  stream.



The user  can  also control the  percentage  of  well  water that  flows  to the



basin stream  by  specifying  the input  parameter CPRJ  as  the  fraction  of



groundwater that bypasses the basin stream.





     The surface soil  and surface water concentrations  are calculated every



year according to Equations  (2-25) and  (2-26).  These  concentrations  also



change from year to  year as a result of wind resuspension of radionuclides,



water runoff,  trench water overflow, the  seepage of  water from the disposal



site surface to the  aquifer.   The amount  of radionuclides released from the



surface  soil  of  the disposal  site to the  surrounding surface  streams  is



calculated  using  the  current year  surface  water  nuclide  concentration,



Cy (Ci/m^);  the area of the disposal  site,  S^S] (m^);  the annual  precipita-



tion rate,  Pa  (m/yr);  the  current year amount  of  trench  water overflow,



VQ (m^/yr);  and a transfer factor,  fr,  as follows
                                     2-61

-------
                            Ws = Mpa SwW                      (2-81)
                              SSTREM = Us Cw                         (2-82)

where Ws (rn^/yr) is the amount of water that enters the surrounding streams
from runoff and trench overflow  during  the  current year of simulation, and
SSTREM  (Ci/yr)  is  the amount of nuclides going along  with  that  volume of
water.  The surrounding streams  in  turn  will  transport the nuclides to the
regional basin stream within the same current year of simulation.

     The total release of radionuclide,  QLBTTH,  to the basin is the sum of
the 10,000 yr releases, i.e.,

                                          9
                        QLBTTH = QDWSB +  EQLB(J)                   (2-83)
                                         J = l

     The population health effects in the regional  basin due to the release
of  residual  radionucl ides  to the basin  are calculated by  multiplying  the
total   release  of  the  radionucl ide  to the  regional  basin by  a conversion
factor, i.e.,

                              HE = QLBTTH-CON                        (2-84).

     When a unit response approach is used,  the total  health effects for
the actual concentration of the waste are calculated  in a  separate health
effects accounting model.   Since the water usage for  each  water  basin is
different   from  one  site  to  another, different  health effect  conversion
factors should  be used.    A detailed  description of  the  health  effects
accounting model  is discussed in a  separate  report on  the  characterization
of health  risks and disposal costs  associated  with alternative methods  for
                                      2-62

-------
 land  disposal  (EEI84).   The health  effects  conversion  factors, which  are



 used  to  determine the health effects to the  regional  basin  population  from



 residual  radionuclides,  are  calculated   independently  of  PRESTO-EPA-POP.



 However,  the methodology  associated with their  derivation  is  included  in



 the following section.





 2.3.2  Conversion  Factors  for  Regional  Basin  Health  Effects





     The  health  effect and  genetic effect conversion factors  are  used  to



 calculate the impacts  of  residual  radioactivity entering a regional surface



 water  drainage  basin  system.    A  number  of  assumptions   must  be  made



 concerning  the  quantity of  water contaminated  with residual radioactivity



 which will  be withdrawn by downstream communities, the population using the



 stream water, and  the uses to which the water will  be put (i.e., drinking,



 irrigation,  etc.).   These conversion  factors are applied to the  residual



 radioactivity entering  the basin  to obtain the number of health effect and



 genetic  effect.





     Per capita water  consumption is calculated  for each site, taking into



 account  the local  irrigation  requirements  and  the  fraction of the  year



 during which irrigation  takes  place  (Equation (2-85)).   For regions  where



 multiple  water  sources  may  be  used,  fractional  correction  factors  are



 applied.   For example,  a portion   of  the requirement  for  the irrigation



 water may  be met  by  using  a  well   or  stream,  while the  remainder may  be



 withdrawn from  a   farm pond with  no  contamination.  This   is  handled   by



 including "switches"  in  the  water  consumption  equation.  Thus  if  half  of



the irrigation water  at  a given  site  is withdrawn  from  a  stream while the



 rest  is gathered from  precipitation-fed farm  ponds,  the  irrigation  pathway




switch will  equal  0.5.






                                      2-63

-------
                 Vu = [3.9x10^^ + UwLh + 1.5xlo4La]Np            (2-85)

where

     Vu   = water used (1)
  3.9xl07 = 4492 m2 irrigated land per person x 8760 hr/yr
     W-j   = irrigation rate (l/m^-yr)
     f-j   = fraction of year when irrigating
     L-j   = irrigating pathway switch
     Uw   = individual water consumption per year (1/person-yr)
     Ln   = human pathway switch
  1.5xl04 = annual  water fed to cattle consumed by humans (1/person-yr)
     La   = animal  pathway switch
     Np   = size of population

     In order to match the per capita water use patterns of the downstream,
basin  population to  those  of the local population,  fractional  usage para-
meters must be included.   For the actual PRESTO-EPA-POP analyses, fractional
usages are modeled for sites where no water  use comes from the well or stream.
The annual per capita water usage by the regional  basin population is given
by

        (Vu/Np)/1000 = per capita water consumption (m^/person-yr)

     It is  assumed  that  the  regional  basin  population downstream  of  the
disposal  site  is directly related to  the  volume flow  rate  in  the stream.
An  average  river basin  generally has  an  annual  river flow-to-population
ratio  of  3000 m^/person.   The  site-specific water usage  rate  (per person)
is  then  compared  to  the  standard rate of 3000 cubic  meters/person-yr to
determine the fraction of  stream flow that will be  used  by the downstream
populations.
                                     2-64

-------
HECFW =
GECFW =
HE
WW + SW
GE
WW + SW
 [Surface Water     1 _  per  person  site-specific  water  consumption  rate  /,,  Rfi\
 Utilization  Factor) =         standard  rate  (3000  m3/person-yr)


      When  the  water utilization fraction  has  been  computed,  it is used  to

 compute the number of  health  effects occurring in the  downstream populations.

 For  each disposal  site,  output data  from PRESTO-EPA-POP  are  analyzed  to

 determine the  number  of health effects  and genetic effects  occurring  in  the

 local  population per  curie  of  each  radionuclide pumped  from  the well   or

 stream.  The water  pathway conversion factors are defined  as follows:


                                                 F                    (2-87)


                                                 F                   -(2-88)
 where
    HECF^ = health effect conversion factor for the water pathway
            (deaths/Ci)

    GECFy = genetic effect conversion factor for the water pathway
            (effects/Ci)

    HE    = number of fatal cancers in the local population over 1000 years

    GE    = number of genetic effects occurring in the local  population
            over 1000 years

    WW    = radioactivity pumped from the well  over 1000 years (Ci)

    SW    = radioactivity pumped from the stream over 1000 years (Ci)

    F     = surface water utilization factor


     For the  health effects  conversion  factor  analysis, the  air pathway

sources were shut  off  for the regional  basin  by  setting spillage  equal  to

zero.    No  on-site farming  or  basement exposures  are  included,  either.

Therefore,  the health effects  in the exposed  population  are  due to use  of

contaminated water only.
                                      2-65

-------
     In addition to water  usage,  there  is  another exposure pathway for the


downstream communities.  The possibility exists that contaminated fish will


be  consumed  by the  downstream  regional   basin  population.   Conversion


factors for  fish  consumption  (health effects/Ci )  were added  to  the water


pathway conversion factor, as follows:



                            HECF = HECFW + HEF                       (2-89)


                            GECF = GECFW + GEF



where



     HECF = combined health effect conversion factor (effects/Ci)


     HEF  = health effect conversion factor for consumption of fish
            (effects/Ci)


     GECF = combined genetic effect conversion factor (effects/Ci)


     GEF  = genetic effect conversion factor for consumption of fish
            (effects/Ci)



     The  health effect  conversion  factors   for  consumption  of  fish  are


calculated in the  following manner:



                            HEFT = ()BfiUi4).                       (2-90)
                            GEF-J  = (£)BfiUf(£).                       (2-91)
                                    K       LI
where
   HEF-j    = health risk from fish consumption  per curie of nuclide i
            released to the river


   P      = population utilizing the river


   R      = river flow rate (1/yr)


   Bfi     = nuclide transfer factor - water to fish (PCl/k9 fish)
                                                     pCi/1  water
                                      2-66

-------
   Uf     = annual fish consumption rate per person

   (D/C)-j = cancer risks per curie of nuclide i ingested by the  population

   GEF-j   = genetic effects from fish consumption per curie of nuclide  i
            released to the river

   (G/C)-j = genetic effects per curie of nuclide i  ingested  by  the population


     The  regional  basin  health/genetic  effects  for  each  nuclide  are

calculated by multiplying the residual  for the radionuclide released to the

downstream  basin  by  the   appropriate   health  effect   or genetic  effect

conversion factor, as follows:
  Basin Health Effects
[Residual-,-  (1st 1000 years) +           (2-92)
 Residual-j  (Years 1001 - 10,000)] HECF-j
  Basin Genetic Effects-j
                        [Residual,- (1st 1000 years) +
                         Residual-j (Years 1001 - 10,000)]
                                        (2-93)
The total  regional  basin health/genetic effects resulting from all residual

nuclides are calculated by summing over all  nuclides (i) as follows:


                                       N

     Total  Basin Health Effects  =     £   Basin Health Effects-;
Total  Basin Health Effects  =
         £
                                           Basin Genetic Effects,
                                      2-67

-------
                  3.   DEVELOPMENT OF PRESTO-EPA-POP CODE
3.1  STRUCTURE AND INFORMATION FLOW





     The  PRESTO-EPA-POP  code is written  in  FORTRAN IV  for  an  IBM 3081 or



comparable  computer   system  and  requires 850K  bytes  of memory.    It is



designed  to process  up  to  40  nuclides  for  a maximum of  10,000 years.



Evaluation  of  local  and  regional basin health  effects  of 31 radionuclides



over 10,000 years takes approximately 7 minutes to execute.  A shorter  test



of ten nuclides takes less than two minutes to execute.  The program should



be easily transferable  to other IBM installations.   It has run correctly



on another  non-EPA  IBM  computer  system  after installation  directly   from



tape.  Non-IBM users  may have to modify the job control language (JCL), the



NAMELIST  inputs  and  other  program segments  where  character manipulations



are used.





     The  PRESTO-EPA-POP  code  is  structured  in  a modular  form to permit



simple upgrading  or  replacement of  given submodels without  rewriting the



entire code.  The subroutine structure of the code is shown in Figure 3-1.





     There are three  classes of submodels:  unit response, scheduled event,.



and bookkeeping submodels.  Unit response submodels simulate processes  such



as rainwater  infiltration through the  intact  portion  of the trench  cap,



erosion of soil overburden  from the trench cover, and atmospheric transport.



Such   submodels  are  usually  accessed only  once  during  a  model   run  and



generate  parameters and  rates used  elsewhere  in the simulation.
                                       3-1

-------
Mf



XPRESS « 	

INFL t 	
[NUCLIOE
LOOP
ROUT (



SOU.


fmuLT

i
l
1 I NUCLIDE


j₯:₯:: ₯:X;X .:X;X
r:SSxS.:;SSS.
xS::₯-x₯x₯x-x-

|:i₯;₯x₯:₯:₯S₯₯
|₯:₯:₯:₯x"-.₯:₯x
,: -x-x: :-: •:•:•••: •:•:; ,
(•:•:•:•:•: -:-x-x •:•:;.•:.:.. NUCLIDE

l-::xXx-x.x :•:;:•:;.
|;:;:₯:Wx₯x.:.-.;x-
f:H:-S::x::₯i':x₯:-j
v₯:Xx₯x₯x₯:₯x
J₯:₯i;:₯:;:₯:₯₯₯₯-,
₯:x;x₯sss-x:|
pgmm
J₯:₯::':'-₯:vS:

[NUCLIOE
LOOP



INUCLIDE

i

i

L



(YE AfliV ~" rwu^LiDl
i LOOP I LOOP

t *NUCLIOE" ~


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i
\
i ]
t L
vlN






























w














*"







	

*-
	







• ^ -.-.,-


r
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• QUANC 8

























IRRK3A

HUMEXA
















DARTAB

	


	 .
LEACH





SUSPNO
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SOURCE


*• AIRTRM

T | 	 »• 3MMA i
i 	 ' — »• YLAG


PTM"! ' " T >| SIGMA ZJ
— — -1 L > YLAG
•> ERORr


... „„ „ ,, .., ... ^



t




t



JL _
i





J


w 	 >• OUT 1
j



,
i









	 F:~— —^•:-^^)
i₯x₯:iS:::₯:.:xv₯:₯x::₯:₯:₯:₯:--j
tv₯:₯:'₯:₯x₯:₯:₯y::;V.₯₯:₯V₯:₯:o
	 iiiiiiiiiiilllii|
x.x-.::-.x:::x:x::::vX.:::::X;::X;X:::j
•••••/•-••'.•'.;".-X.;'.;'. ;'.;'. v';'.;'.;'-:. ;.-..:-:.:-:•:•:-:•

I1 	 --.•.-.-.-.--.-.- 	
... .-.;....;..;.;.:.:.;.............. .....:.-.;.: :.
X:.-:X:₯:'x₯:::v:::;x₯x₯x₯x₯:.::l
'••'•'•'•'• S₯':₯x'₯::^:₯x£::₯x'₯r:'- 1
^:^x. — '.^.,--^. •- —:— Jv-^^lxlilillOliS : '•''
                                            RAE-102122
FIGURE 3-1.  PRESTO-EPA-POP SUBROUTINE STRUCTURE,
                       3-2

-------
     Scheduled  event  submodels estimate events  such  as  the time of trench



cap failure, while bookkeeping  submodels determine the water balance in the



trench  and  radionuclide  concentrations   in  the  trench  outflow  and  the



aquifer.   Output  from the bookkeeping  submodels is  iterated annually over



the  simulation  period.   Risk evaluation  bookkeeping  submodels  accept the



cumulative  or  mean   output  from  the  transport  portion  of  the  code  and



generate doses and population  risks,  based on a  life-table  approach.










3.2  SUBROUTINE DESCRIPTION





     An  alphabetical  listing  and  description of the  subroutines  and  main



program found in PRESTO-EPA-POP is given below.





     MAIN  - This  routine  is  the main calling program of PRESTO-EPA-POP and



defines the most  commonly used variables  of  the code,  specifies dimension



and common  areas,  and initializes variables  and input  control  parameters.



The input  and  output  subroutines,  SOURCE  and OUT,  are  called  directly  by



MAIN (Figure  3-1),  as are the  unit  response  model  subroutines  AIRTRM,  and



ERORF.    MAIN  also  calculates:  the vertical water  velocity;  retardation



factors; vertical,  horizontal  and  total transit  times  in  groundwater  (the



transfers  from  trench to vertical  soil column  to aquifer  in  Figure 2-1);



and the  basement  exposure correction  factor  (Section 2.2.2).   The decay-



dispersion  correction  factor,  DDETA  (Hu81),   is   calculated   for  each



radionuclide  in  MAIN  (factor  DDETA adjusts  the activity  output  of  the



aquifer  for  the   combined   interactions   of   longitudinal  dispersion  and



radioactive decay.)   QUANC8, which  is based  on an eight panel  Newton-Cotes



rule,  performs the integration necessary to obtain the correction factor.
                                   3-3

-------
     MAIN calls the bookkeeping subroutines to calculate quantities associ-



 ated with trench  water  balance,  trench  cap status, changes in  land use  and



 basement occupancy.  Other subroutines called by MAIN compute the amount  of



 leaching from  trench,  transport  of soluble surface components, atmospheric



 concentrations,  and well  concentrations.    In  addition,  aquifer  volume,



 hypothetical  radionuclide  withdrawal  from well, and  material  balances  for



 water in the aquifer are calculated in MAIN.





     Risk evaluation  submodels called  from  MAIN  account  for radionuclide



 concentrations in  food  due to  atmospheric  deposition  and water irrigation,



 and  radionuclide  intake by man.   These  subroutines are IRRIG, FOOD, HUMEX,



 CV,  COV,  IRRIGA,  FOODA,  HUMEXA,  CVA,  AND  COVA.    Finally  DARTAB,  which



 creates tables  of predicted health  effects  from  radioactive  effluents  is



 called from MAIN.





     The annual  simulation  loop  and the  radionuclide loop are executed a



 selected number of  times.   During a model run, MAIN  may  access any or all



 of  the  subroutines or  functions which  are   listed  below  in  alphabetical



 order.





     Average concentration values  printed  in the  concentration tables  are



 computed in  the MAIN routine  using a summation calculation within  the  MAXYR



 loop (the  principal yearly iteration loop).   After  this  loop  is completed,



 the summed concentration values are divided by the number of years considered



 in  the  simulation  and  the  results are  printed.    Maximum  concentration



 values  are  identified  by comparing  stored  concentration values  to  the



values determined  in each  iteration of the yearly  simulation  loop.   If the



new concentration  is  greater, then the concentration and  corresponding year



number are stored  for printing  in  the concentration tables.
                                   3-4

-------
      AIRTRM   -   This   subroutine   is  the  main   calling  program   for   the



 atmospheric  transport submodel.   AIRTRM  calculates  sector-averaged  (22.5



 degree)  atmospheric exposures  normalized  to the  source  strength.   AIRTRM



 and  all  its supporting  subroutines  are adaptations  of  the interactive



 Gaussian  plume  atmospheric model, DWNWND  (FiSOa).   AIRTRM  also calculates



 the  deposition  rate onto  surfaces per unit source strength.   To-make these



 calculations, AIRTRM  accesses four  other  subroutines,  SIGMAZ, DPLT, YLAG,



 and  SIMPUN,  and  utilizes a number  of  user-input parameters including source



 height,  lid  height, stability class, type of stability class formulation,



 Hosker roughness parameter, wind velocity, deposition velocity,  gravitational



 fall  velocity, and  source to  receptor distance.  The normalized atmospheric



 exposures  are  returned to the main  program  and  are  used  in later dose and



 risk  calculations.





      CAP  - This function calculates  and  returns to  both MAIN and TRENCH,



 the  fraction of  the trench  cap that  has failed.  Cap failure may be either



 partial or total.   Total failure may  be caused by erosion of all overburden



 as calculated  by ERORF.   Partial  failure indicates that a  portion of the



 cap  has been completely  removed;  the remainder of the cap is  still subject



 to erosion.  Partial  failure  may  be  caused by user input of the end points



 of a  linear  function  to selectively  remove  all  overburden  from a fraction



 of the trench.





     COV, COVA - These functions  are called  by subroutine IRRIG and IRRIGA



to calculate radionuclide concentrations in vegetables, milk,  and meat that



may be contaminated by irrigation.  The radionuclide concentrations in food



depend on  such  quantities  as the  agricultural  productivity of vegetation,



the period of irrigation annually, the storage delay period between harvest
                                    3-5

-------
 and  use for  pasture  grass,  feed,  leafy  vegetables  and  produce,  and  the



 radionuclide decay constant.





     CV, CVA  -  These  functions are utilized  by  subroutines FOOD and  FOODA



 to  calculate  radionuclide  concentrations in  pasture  grass and stored  feed



 consumed by animals, and in leafy  vegetables and  produce  consumed  by humans.



 CV  is  essentially the  same as function  COV, except  that CV  is used  for



 atmospherically deposited  radionuclides  and  COV  accounts for radionuclides



 deposited  by  spray  irrigation.   Pertinent input  data include agricultural



 productivity,  fraction  of  the year  vegetation   is  exposed  to   depositing



 radionuclides,  and  the  delay  time  between  harvest  and  consumption  for



 stored feed, pasture grass, leafy vegetables,  and produce.





     DARTAB -  The original DARTAB  code  is  a self-contained  program which



 combines  radionuclide  environmental   exposure   data  with  dosimetric   and



 health effects  data  to  create tables  of predicted impacts  of radioactive



 effluents.   DARTAB  has  eleven subroutines  and  contains  over  3000 FORTRAN



 source statements.   DARTAB subroutines are RDSTOR, FACOUT,  CHLOC, PREPDR,



 PREPRF,  PREPHR,  MULT,  DRTAB,  ORGFAC,  SUMMRY, and  SUMMR2.  These  are  not



 discussed  specifically  in  this report.   For  information on  the original



 DARTAB consult  the  document describing the code (Be81).   DARTAB has been



modified for PRESTO-EPA-POP so that  the program is treated as a subroutine.



 Environmental  exposure data are now passed in COMMON  from MAIN to DARTAB's



subroutines.





     DARTAB uses dosimetric and health effects data from the methodologies



of RADRISK  (Du80).  RADRISK uses  a  life-table model to calculate the human



health  risk to  a cohort  of  100,000 people from a  constant input of 1 pCi/yr



 (0.037  Bq/yr)  via  ingestion and inhalation over a lifetime (70.7 yr).
                                   3-6

-------
     These   intake   conditions  are   approximated   in  PRESTO-EPA-POP  by



calculating  an  average  intake  over the span of the assessment of each type



of intake.   RADRISK data files are accessed directly by DARTAB.





     DPLT -  The  subroutine  DPLT  is called by AIRTRM and computes a correc-



tion  factor  for  plume  depletion.   To  make  this  calculation,  DPLT calls



subroutines  SIGMAZ and SIMPUN.






     ERORF - This  subroutine uses the universal  soil  loss  equation, USLE,



developed  by  the  U.S.  Department  of  Agriculture  (USDA61)  to  determine



sediment  loading  for rain-driven surface erosion.   Estimation methods  and



tabulations  for factors used in USLE have been published (McE76).  The code



user inputs  all six of these factor values.  The calculated erosion rate is



returned to  MAIN where it is converted to an annual erosion rate in meters.



This  erosion rate is  utilized by MAIN  to  determine the thickness  of  the



cap.





     FCN  -  This  function  subprogram  returns  to  QUANC8  a  functional



evaluation  of   the  integral  used  in  calculation  of   the  aquifer  decay-



dispersion correction factor.   The routine is written  in  double  precision



to facilitate interaction with the double precision routine QUANC8.





     FOOD, FOODA  - Subroutine  FOOD is called  only  once per simulation  and



calculates   the  average  concentration   of  each  radionuclide   in  foods



contaminated by  atmospheric deposition  and  root  uptake.    The  deposition



input  to  FOOD  is calculated  in  subroutine  AIRTRM.    The equations  and
                                    3-7

-------
internal parameters used  by  FOOD are those  in  AIRDOS-EPA (Moo79).  Output



from FOOD  is  used  by  the subroutine HUMEX  to  calculate the human exposure



via ingestion of these contaminated foodstuffs.  Subroutine FOODA is called



from MAIN each simulation year.





     HUMEX,  HUMEXA -  Subroutine  HUMEX  accepts  user  input  and  receives



averaged data from subroutines AIRTRM,  FOOD, IRRIG, and VERHOR to calculate



the average  annual  human exposures  via  ingestion  and  inhalation.   Output



from HUMEX supplies the input to the DARTAB subroutines for calculations of



risk  and  dose  and tabulation  of  health  results.   Subroutine  HUMEXA  is



called from MAIN each  simulation year.





     INFIL - The  subroutine  INFIL is based  on  a model  by Hung (Hu83b) and



calculates  annual   infiltration  through   the   trench   cap.    INFIL  calls



subroutine SOIL and ROUT.    Inputs  to  INFIL include  hourly precipitation,



daily temperature, and various trench cap characteristics.





     IRRIG,  IRRIGA  -  Foods  may  be  irrigated with  contaminated  water  from



either  surface  or groundwater  sources.    Input  to IRRIG, which  is  called



only   once   per   simulation,   includes   the   time-averaged   radionuclide



concentrations in  well or surface water calculated by  VERHOR or subroutine



SURSOL, respectively.   IRRIG calls  the function COV  and uses the equations



in AIRDOS-EPA  (Moo79,  FiSOb) to calculate  the  time-averaged concentration



of each  radionuclide  from direct  deposition by irrigation  and  subsequent



root  uptake  in foodcrops.    Subroutine  IRRIGA is called  from  MAIN  each



simulation year.






     LEACH -  Subroutine  LEACH calculates  the  amount of  each  radionuclide



from the  homogeneous  trench  contents  that  leaves the trench  each  year.
                                   3-8

-------
Losses may  be  via transport through  the  trench  bottom or by overflow from
the trench.  There  are five independent user-specified methods that may be
used  to  calculate  these amounts:   the option  is  chosen by  specifying a
value  from  one  through five  for  parameter LEAOPT.   Table 2-2  lists the
calculational methods  corresponding to values of LEAOPT.  The total-contact
options,  1  and  3,  assume  that all  of the  trench  contents have  been  in
contact  with  water  during  the  previous   year.    The  immersed-fraction
options, 2  and  4, assume that  the  wetted  fraction  of  the waste equals the
ratio  of maximum  water level  to  the trench  depth.   The  distribution
coefficient   options,   1 and  2,  utilize  a  K,j   approach  to calculate  the
radionuclide concentrations released from  the  wastes  to the  water, while
options  3  and  4  use   a  solubility  estimate  rather  than  K
-------
     ROUT   This subroutine is called by INFIL.





     SIGMAZ - This  subroutine  is  called  by both AIRTRM and DPLT to compute



the vertical atmospheric dispersion parameters.  Depending on the choice of



parameterization specified in the input data set, SIGMAZ will calculate the



dispersion  parameters   by  one  of  eight   schemes.    Necessary   input  data



include the downwind distance, stability class, Hosker roughness parameter,



and  lid  height.   Other data  necessary  for Lagrangian  interpolations (by



function YLAG)  are  contained  internally  in SIZMAZ  and need not  be input by



the user.





     SIMPUN - This  subroutine, originally written  by  Banish  (Bar70),  uses



Simpson's  rule  to  integrate  along the   ground  level  centerline  of  the



atmospheric plume to compute  the  depletion fraction.  All  input to SIMPUN



is  supplied by  DPLT,  the  subroutine that calls SIMPUN  and to  which the



results are returned.





     SOIL - This is a  subroutine called by ROUT.





     SOURCE - Subroutine SOURCE reads the  input  required  to  initialize and



quantify transport  parameters, except those  required  for subroutine INFIL.



Data concerning  program  control,  climatic  description, trench description,



aquifer description, atmospheric description, site-surface description, and



radionuclide description are  read  in  by  SOURCE.   SOURCE also  prints out



these data before  any calculated results  are output.





     SURSOL -  Subroutine SURSOL computes  the amount  of soluble radionuclide



that enters the stream  annually.   Input  variables to SURSOL  include the
                                  3-10

-------
average  depth  of  active  exchange  in  the  soil,  the  average  downslope
distance to the stream, the cross slope extent of  the spillage, the average
annual infiltration, the  bulk  density  of  soil, the amount of spillage, and
the  surface  soil  distribution coefficients.   Variables output  from SURSOL
include the  amounts  of radionuclide going  to  the  stream and the deep soil
layers and the  radionuclide concentration  in the interstitial water of the
contaminated surface region.

     SUSPND  -  This  subroutine  calculates  the  above   trench  atmospheric
source  term  from the  ground  surface by  two  methods, a  time-dependent
resuspension factor  and a resuspension rate due to mechanical disturbance.
Input variables include the current year of simulation, the spatial  area of
the  contaminated   surface,  the  radionuclide  concentration  on  the  ground
surface,  the  beginning and ending years  of  mechanical  disturbances,  the
resuspension  rate,  and  the  wind  velocity.    SUSPND  assumes  that  all
radionuclides to  be resuspended  are  deposited  on the soil  surface  at  a
simulation  time  zero.    The  resuspension  factor  calculated  uses  the
empirical  equation of Anspaugh et al.   (An75).

     The atmospheric source term is returned to MAIN and is used along with
X/Q to calculate  the air  concentration of  each  radionuclide  available for
deposition onto  foodstuffs and for  inhalation by  the  general  population.
The value of X/Q is calculated by AIRTRM.

     TRENCH - This subroutine  determines  the  trench water  balance.   Input
variables   include  trench  dimensions,  porosity and permeability  of  trench
contents,   trench   water   volume  from  the  previous year,  length  of  the
saturated   zone,  and  annual  precipitation  and infiltration.    Output  from
                                  3-11

-------
TRENCH  includes  the maximum  depth  of water  in  the trench,  the  volume  of



water  in  the  trench,  volume  of  water  overflowing  the trench,  and water



volume lost from the bottom of the trench.





     The  amount  of  water which  overflows  the  trench,  is  calculated  by



comparing the  maximum water  depth to the  trench  depth  and overflowing any



amount greater than  the  trench volume.  The  variables  VOLO, VOLB, OLDWAT,



and DMAX  that  quantify  overflow,  bottom loss, water  level  during previous



year,  and maximum  water  depth in  trench,  respectively,  are used  by  the



subroutine LEACH, discussed previously.





     VERHOR  -  This  subroutine  calculates and  decays  the  amount of  each



radionuclide,  that  reaches the irrigation/drinking  water  well in a given



year.   Variables  evaluated  elsewhere  in  the code  and  input   to  VERHOR



include the current year of the simulation, transit time from the trench to



the well,  the volume of  water leaving the trench  bottom, the amount of each



radionuclide leaving the  bottom of  the trench, the  amount  of radionuclide



reaching  the  aquifer  from  the   contaminated  surface  region,   and  the



radioactive decay constant.





     YLAG  -  This  function performs  a  Langragian  interpolation as part of



the atmospheric  transport  calculations.   The original  program was  written



by Brooks and  Long (Br70) and adapted  for use here.   All  input data  are



supplied by  subroutine SIGMAZ.





     XPRESS  - This  subroutine computes and  stores  exponential  decay factors



to be used  repetitively  in the nuclide  loops.  XPRESS  saves  a substantial



amount of  computing time.
                                  3-12

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            4.    DESCRIPTION  OF  OUTPUT  OF  THE  PRESTO-EPA-POP  CODE









      The output of the PRESTO-EPA-POP code is designed to be self-explanatory



 and  provide  descriptive  comments, definitions,  and  intermediate tabulations



 for  a comprehensive description of the model  simulation.   The output  from



 PRESTO-EPA-POP  is described in the following sections which correspond  to



 the  output  sections contained  in the  printout  for a run.   Full details  on



 operation of the PRESTO-EPA-POP code  together with sample problem  runs and



 a  source  code  listing  are  given   in   the   PRESTO-EPA-POP Users Manual



 (EPA85b).









 4.1   REPLICATION OF  INPUT DATA





      The first  section of the  code output  prints  all  input  data,  with the



 exception of the input data  for the subroutine, INFIL.   Input data  are  read



 and  then  written  on  a  temporary  storage  device   and  then  on the output



 device.   This record  of the input data  set  is printed  out for  reference



 identification of  the run and  verification of  the  input data.   Input data



 is subsequently  read from the temporary storage device for use by the code.



 INFIL  input  data  is treated  separately  as  shown  in  Section  4.4.   This



 approach preserves the modularity of the INFIL subroutine.










 4.2  ORGANIZATION OF INPUT DATA





     In the  second section   of  the  output of the  PRESTO-EPA-POP  code, the



input data  are organized and  summarized according to data  type and transport



subsystem or pathway  and then  printed out.   A  detailed description of the
                                    4-1

-------
input  data  together  with  sample  computer   runs   can  be  found  in  the



PRESTO-EPA-POP User's Manual (EPA85b).





     The  first  part of  this  output  section  consists of the  computer run



identification and  the user-supplied  identification from the  first  input



card.   The control  information output  identifies the site  and interprets



the  run  control  data  entered.   These control  data  include  radionuclide



leaching options, trench  cap  failure data, and water  use  parameters.  The



trench information  output describes the trench area and depth,  the porosity



of the trench contents, and the annual infiltration for the watershed.





     The aquifer information  output defines the  groundwater velocity,  the



trench  to  aquifer  distance,   the   trench  to  well   distance,  the  aquifer



thickness  and contamination plume  dispersion  angle, the porosities of  the



sub-trench area  and  the aquifer,  the sub-trench permeability.





     The  atmospheric   information  output  describes  the  effective  source



height for the  wind-blown mechanically mobilized contamination  plume from



the site, the gravitational fall  velocity  of  suspended  soil  particles,  the



site-to-population  distance, the  lid height,  the Hosker surface roughness



factor,  the  atmospheric  stability  class   and  dispersion  formulation,  the



fraction of the time wind blows  toward the population, and  the parameters



specifying the resuspension factor  and resuspension  rate.





     The surface information  output  consists of  the universal  soil  loss



equation parameters, the surface  soil porosity and bulk density, the runoff



fraction for  rainfall,  the stream or  river  flow rate, the cross-slope extent



of  spillage,  the active  soil depth, and  the average distance from  the



trench to the stream.  The  air and  food  chain information  output describes
                                    4-2

-------
productivity data  for  grass  and vegetation, timing data for computation  of



radioactive decay for the ingestion exposure pathway,  and nuclide weathering



and carbon-14 equilibrium data.  The water-food-chain output describes data



which  characterize water use  by milk  cattle,  goats,  and  beef cattle and



water  use for crop irrigation.





     Finally,  the  human  ingestion  and  inhalation   rate   information   is



printed.









4.3  RADIONUCLIDE SUMMARY TABLES





     A set of three tables under the nuclide information heading summarizes



radionuclide data used for the transport calculations.  First, an inventory



table  specifies  the  initial  inventory in the trench,  on  the soil  surface,



in  the  stream,   and  in the   atmosphere.    Included  in  this  table  are



radioactive  decay  constants  and  the  solubility  constants.   The  second



table  summarizes the  chemical  distribution coefficients  for  the  surface



soil, the trench contents, the  vertical  soil column,  and  the aquifer.  The



third  radionuclide  table summarizes  the seven  radionuclide-specific  food



chain parameters used  by the FOOD, IRRIG,  HUMEX,  CV,  and  COV subroutines.



These parameters are also used  by  the  FOODA,  IRRIGA,  HUMEXA, CVA,  and COVA



subroutines.    Radionuclide  atomic  mass numbers  are  extracted  from  the



radionuclide  names  and used in  the calculations.   Results from the  mass



extraction algorithm are printed in the initial  calculations table.
                                   4-3

-------
4.4  INFIL INPUT/OUTPUT





     The  fourth  section 'of output  of  the code consists  of  the input data



and results produced by the subroutine  INFIL.   INFIL control  data are given,



followed  by  monthly average  values for  hours  of sunshine,  daily average



temperature levels, and hourly rainfall amounts.





     The  trench  characteristics  presented are  the  snowmelt coefficient,



trench  cover  thickness,  width,  slope,  permeability,   porosity  for gravity



and pellicular water,  equivalent  upward  diffusivity,  and equivalent upward



hydraulic conductivity.  The  INFIL  time  step  is  also  printed.  Results are



annual precipitation, evaporation, runoff, and cap infiltration.










4.5  UNIT RESPONSE CALCULATIONS





     This output  section includes results of nuclide-specific annual trans-



port calculations which will  be  used by  the  bookkeeping submodels for each



simulation year.    The  outputs also includes  soil  loss  calculation results



and the calculated or input value for the ratio of atmospheric radionuclide



concentration per unit  release rate at  the radionuclide disposal site.









4.6  ANNUAL SUMMARY TABLES  FOR SPECIFIED YEARS





     Control  variables  determine the years for which  results will be given.



For those years,  a number  of hydrologic and transport  variables are output.



Included are trench cap status, maximum possible water depth in the trench,



water loss by overflow and drainage  from  the  trench,  and trench inventory.



Radionuclide concentration  values  and  flux  values are presented  for key



pathways and regions of interest.
                                   4-4

-------
4.7  RADIONUCLIDE CONCENTRATION TABLES





     The radionuclide concentration tables present, by nuclide, the  average



concentration  over  the  entire  assessment  period,  the  year  of  maximum



concentration,  and   the maximum  concentrations  for  the  atmosphere,  well



water,  and  stream water.   Because human  exposures may  commence and peak



many years  after  closure  of  a disposal  site, the year and level  of  maximum



concentration  are important  since  they are  related  to the  year at which



population  exposures are most significant.





     Separate  average  radionuclide  concentration  tables  for   the user-



specified  averaging  time period  are  included.   These tables  present  the



radionuclide   concentration   in   five   types   of   foods   resulting  from



atmospheric nuclide deposition and irrigation.










4.8  RADIONUCLIDE EXPOSURE TABLES





     Annual  population  intakes   of  radionuclides  by  ingestion  and  by



inhalation  are output  and  the  fraction  of  ingestion  dose  from drinking



water is given.   The  radionuclide  exposure  tables list by nuclide the year



of  maximum exposure  and  the corresponding  level  of  the   maximum,  mean



population  exposure  from  the  atmosphere,  the   ground   surface and  for



ingestion and for inhalation.  Although the exposure terms are dependent on



the  concentrations  summarized in  the  concentration  tables, the  times  of



maximum  exposures  will  in   general  differ  from the  times  of  maximum



concentrations.   This  difference  occurs  because  of  the   dependence  of
                                    4-5

-------
exposure  on   soil   concentration   and   the  nuclide-specific  uptake   and



concentration mechanism of the food chain which are considered  in  computing



exposures from ingestion.









4.9  DARTAB CONTROL  INFORMATION





     DARTAB control  information includes run identification data,  summaries



of output table  control  information,  lists of  critical  organs and cancers



to  be  considered  in the  run,  dose  equivalent factors  for  low  and  high



linear energy  transfer  (LET) radiation, radionuclide  uptake  and  clearance



data, and lists of nuclides and organ  dose or cancer risk factors  not found



in the  RADRISK data sets  which were  accessed by DARTAB.   The location of



the  population  at risk, the  lifetime fatal cancer  risk  at that  location,



and the organ dose weighting factors are also given.









4.10 DARTAB DOSE TABLES





     DARTAB  dose  tables   are  produced  in  the  code   output   and present



individual and collective  dose summary  rates  by low and high LET  radiation



and organ, by  low and  high LET radiation  and  exposure pathway, and by  low



and high LET radiation  and radionuclide.  Both absolute dose and percentage



of total  dose are included in these tables.










4.11  DARTAB  FATAL CANCER RISK TABLES





     DARTAB   fatal   cancer   risk  tables  produced   in   the  output present



individual  and collective  fatal cancer  risk,  premature death, and  lifetime
                                   4-6

-------
fatal  cancer risk exposure  equivalent.   Genetic  risks  are also summarized.



Values are summarized by  low  and  high  LET radiation, by organ, and also by



pathway.










4.12 RESIDUAL RADIOACTIVITY RELEASED TO THE BASIN AND HEALTH EFFECTS





     This output section gives that amount of radionuclides released to the



basin each  millenium during  the  10,000 year  simulation.   The  aggregated



total  release  of each  radionuclide,  the health effect  conversion factor,



and the  basin population health effects by radionuclide are given.
                                    4-7

-------
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        Phys.  29:571-582,  1975.

 BaeSl   Baes,  C. F.,  Ill,  and R. D.  Sharp,  "A Method for Determination  of
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 Bae82   Baes,  C.  F.,   Ill,  R.  D.  Sharp,  A.  L.  Sjoreen  and R.  W.  Shor,
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 Bar70   Barish,  J.,  The  Computing  Technology  Center  Numerical   Analysis
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 Be81   Begovich,  C. L.,  K.  F.  Eckerman,  E.  C. Schlatter,  and  S.  Y.  Ohr,
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 Br70   Brooks,  A.   A.,  and  E.   C.  Long,  The Computing Technology Center
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Cla78   Clap, R. B.  and  G.  M.  Hornberger, Water Resources Research  Journal,
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                                  R-l

-------
Ec81   Eckerman,  K.  F.,  M. R.  Ford,  and S.  B.  Watson, Internal Dosimetry
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                                  R-2

-------
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 FiSOb   Fields,  D.   E.,  C.  W.   Miller,  and  S.  J. Cotter,  "Comparisons of
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        meetings of  Americal Geophysical  Union,  San Francisco,  California,
        Abstract in  EOS 61(46),  p. 971, December  1980.

 Fi81    Fields,  D.   E.,   C.  W.  Miller,  and  S.  J.  Cotter,  "Comparison of
        Observed  and   Predicted  Sector-Averaged  Air  Concentrations  for
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                                  R-3

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                                      R-6

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Se80   Sehmel, G. A.,  "Particle  and  Gas  Dry Deposition:   A Review," Atmos.
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                                       R-7

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Wi65   WTschmeier  W.  H.  and  D.  D.  Smith,  "Predicting  Rainfall-Erosion
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                                    R-8

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                  APPENDIX A
 A MODEL TO SIMULATE INFILTRATION OF RAINWATER
THROUGH THE COVER OF A RADIOACTIVE WASTE TRENCH
  UNDER SATURATED AND UNSATURATED CONDITIONS

-------
                                APPENDIX A


     This  appendix  contains  the  background  theory  of  the  infiltration

submodel  (subroutine  INFIL)  used  in  PRESTO-EPA-POP  as   developed  by Hung

(Hu83).  Hung's analysis follows.


               A MODEL TO SIMULATE INFILTRATION OF RAINWATER
              THROUGH THE COVER  OF A RADIOACTIVE WASTE TRENCH
                UNDER SATURATED  AND UNSATURATED CONDITIONS


                               INTRODUCTION


     The  disposal   of  low-level   radioactive   wastes  by  the  shallow  land

burial  method  has   been  used  for decades.   An important  consideration  in

evaluating  the performance  of   a waste  disposal  site   is  the  potential

effects  on  the  health  of  nearby populations.    Since   one  of the  major

driving  forces  in   causing the  release of  radionuclides is the  rainwater

which  infiltrates  through  the  cover of  a  disposal trench,  simulating  the

infiltration  process  is  an  important  part of  any  model  for  evaluating

health effects.


     An accurate model  for simulating the infiltration of rainwater through

a trench  cover involves the modeling  of  three flow  systems:   an  overland

flow system, a subsurface flow  system,  and  an  atmospheric diffusion system.

The  overland  flow  system  receives the  rainwater  and  diverts the  excess

water from percolation  and evaporation  into the  receiving drainage system.

The subsurface flow system receives the percolated  water from  the  overland

flow system and transports the  water either downward  as infiltration into

the  trench  and/or  upward  as  evaporation   into  the  atmospheric  diffusion

system.   The  atmospheric diffusion  systems  receives water/vapor  from  the

overland flow system or  subsurface flow system and transports  the  vapor to
                                  A-2

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 the  atmosphere.   One of the  early efforts  in  simulating this  system  for

 storm  runoff was  the Stanford  Watershed  Model  conceived  by Crawford  and

 Linsley  (O66).   The same  model  was    significantly improved by  Moore  and

 and  Claborn  (Mo71)  and  Hung and Keifer (Hu77).  However,  these  models were

 developed  for  water  resources  planning   purposes  with  emphasis  on   the

 overland  flow  system.  Significant improvements  are required to  apply  the

 same  models  to the  simulation  of  trench   cover  infiltration.   This study

 presents  an  efficient  and  yet  accurate   infiltration  model  based  on   the

 dynamic equations governing the  above  systems.

                                 BASIC  EQUATIONS

     The  simulation  of rainwater  movement  through a  homogeneous  trench

 cover, defined  here  as  the  "total infiltration system," involves  analyzing

 the hydrologic processes of overland flow,  subsurface flow, and  atmospheric

 diffusion systems.   The basic  momentum and continuity  equations  governing

 these  three  systems  have  been studied thoroughly  by  other  investigators.

 They are discussed below.

     Overland  Flow  System  -  The  one-dimensional  momentum  and  continuity

 equations governing an overland flow system are expressed by  (Iw64),
and
                      8h      9u    ah
                         + h     + U   = P ' E°
where
     u    =  velocity of overland flow

     h    =  depth of flow


                                   A-3

-------
     a    =  average inclination of the trench cover



     n    =  Manning's coefficient of roughness



     P    =  rate of precipitation



     E0   =  rate of evaporation from the overland flow



     q0   =  rate of percolation from the overland flow system



     g    =  acceleration potential  due to gravitational force



     x    =  space coordinate along the slope of the trench cover



     t    =  time





The above  equation  is derived  from  the  assumptions that  Corioli's  energy



correction  factor,  Boussinesq's momentum  correction  factor,  and  Jaeger's



hydrostatic  pressure  correction  factor  are  all  unity;;  the  flow is  one



dimensional, i.e.,  the  velocity  component  in  the  longitudinal  direction



predominates the velocity component in lateral directions,  and the flow is



a  gradually varied  flow.    The above  system equations  cannot be  solved



independently and must  be  coupled with  the  basic equations  governing  the



other two systems.





     Because Manning's law of resistance is  an  empirical  formula developed



for open-channel flow, it  is  conceivable that the application of  the same



law to  a  thin  overland  flow  may  be questionable.  However,  comprehensive



laboratory and  field studies conducted by Takasao and  Kishimoto (Ta61)  and



Ishihara and Takasao  (Is62,Is63)  indicated  that  the  Manning  Law  can also



reasonably  be   applied  to  an  overland  flow  system.    This   finding  was



confirmed by Foster, Huggins,  and  Meyer (Fo68) and Hjemlfelt (Hj81).
                                   A-4

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      Subsurface  Flow  System  -  The  movement  of  soil  moisture  in  a  subsurface
flow  system  can  be either upward or downward  depending on the  direction  of
the  potential head  gradient.    In  general,  the moisture  in  the  soil   is
simultaneously  transported  in  both  liquid  and  vapor  phases.    The basic
equation  governing this system  has  been derived  by  Currie (Cu61)  and Hi 11 el
(Hi80).    The results  of their  studies  for  the  momentum  and  continuity
equations  are summarized  as  follows
                       q = _DL  (W)+ K(W)  - bD -                    (A-3)
                                  9z              9z
and
                                 aw
                                      -                               <*-<>
where
     q    =  flux of moisture in the vertical direction
     W    =  volumetric wetness of soil
     K    =  hydraulic conductivity
     D|_   =  hydraulic diffusivity
     b    =  conversion factor for transforming the vapor flux into liquid
             water flux
     D    =  diffusivity for water vapor
     C    =  concentration of water vapor in the air-filled void

The above equations were  based on  an  isothermal  condition and assumed that
both viscous flow  in  the liquid phase  and  diffusion  of vapor are impelled
by the  force field of  capillarity and  gravity.   No  explicit  account  has
been taken of osmotic  or solute effects on vapor pressure.  In reality,  the
upper layer  of  the soil  surface is warmer  during the daytime  and  cooler
                                   A-5

-------
 than  the  deeper  layer  during  night  time.   The movement of vapor due  to  the
 thermal  gradient effect  tends  to  be downward  during  the  day  and  upward
 during  the night.   Therefore,  the  error due  to  the  assumption  that  the
 system  is  isothermal may compensate each other within the same day  and will
 not significantly affect the accuracy of simulation.

      Atmospheric  Diffusion  System  -  The  atmospheric  diffusion   system
 transports  the  water vapor through the  turbulent  boundary  layer  into  the
 atmosphere.  The  vapor transport through an unsteady turbulent boundary layer
 involves the analysis of the time-averaged boundary layer equations for  the
 air stream  and the  continuity equation  for the  water vapor.   This analysis
 is extremely complicated.  However,  by assuming  the system is quasi-steady,
 the  solution  of  the system equation  is   obtainable.   The  "quasi-steady"
 technique has been commonly used in solving unsteady mass transport systems.
 It assumes that within  a small time  increment the flow of the carrying fluid
 is steady and that the  effect  of the change from one flow state to the other
 due to the change in time step is negligible.  By imposing the above assump-
 tion, the  water  vapor  flux within  the  fully developed boundary  layer was
 expressed by employing  Pick's  law  for  diffusion  (Bi66)  as
                            j  =  _k2y2 ^/  dCb                        (A_5)
where
     J    =  water vapor  flux
     k    =  Prandtl's  mixing  length  coefficient
     v    =  time overaged  wind  speed
     C^   =  concentration  of  water vapor  in  the  boundary  layer
     y    =  distance from  ground  surface
                                   A-6

-------
                   BASIC  EQUATIONS FOR THE  PRACTICAL  METHOD






     Theoretically,  the  basic  equations  compiled in  the previous  section



can  be  solved  numerically.    However,   the  processes   of   analysis   are



complicated  and  consume  excessive  computation time.   Several  attempts have



been  made  to  solve  a  simplified  system.   For  example,  a conjunctive



overland-subsurface  flow model  without  atmospheric diffusion  system  has



been developed  by Akan  and  Yen (Ak81), and  a subsurface flow-atmospheric



diffusion model without  overland flow system  was  reported by Hi 11 el  and  van



Bavel  (Hi76a)  and Hillel  (Hi76b).    The  above models  solve  the dependent



variables  as  functions  of  space  and  time  and   involve  long  and  costly



calculations if the  real time of simulation is prolonged.  For example,  the



time increment  used  in Akan and Yen's  overland  flow system was  30  seconds



which would  require  excessive  computation  costs  if the simulation were  for



a year or more.





     One may simplify the above system equations  by transforming all  of  the



space-dependent   variables   into  space-independent   variables   to   avoid



time-consuming simulation.  The transformation for each system is described



in the following sections.





     Atmospheric Diffusion System -  The solution  of  Equation  (A-5)  depends



on many  complicated  fluid  dynamic  and boundary  conditions.   One  of the



simplest solutions is  obtained  by assuming  that  the  vapor flux will  not be



limited by the availability of vapor transmitted  from the subsurface system



or the overland flow system.   The  vapor flux under this condition is known



as the evaporation potential  and is  normally  used as the upper bound of  the



evaporation  rate from the  overland  flow and  subsurface  flow systems.   The



actual  evaporation rate  from these  systems  may then  be calculated from  the
                                    A-7

-------
 conjunctive  system to be discussed  later.   The solution  of  Equation (A-6)

 under  the  above  condition was  proposed  by Rohwer  (Ro31)  as


               Ep  =  0.372(1-0.000374pa)(l.  +  0.6Vw)(es  - ea)           (A-6)


 where


     Ep    =  evaporation potential

     pa    =  atmospheric pressure

     Vw    =  wind  speed

     es    =  saturated vapor pressure

     ea    =  vapor pressure in the atmosphere


     Equation  (A-6)  requires time-dependent input for atmospheric  pressure,

 wind  velocity,  and  vapor  pressure  to  compute the  diurnal   variation  of

 evaporation  potential.   The  above  information  is  normally  not  readily

 available  from existing  records.   Therefore, from a  practical viewpoint,

 the computation  of evaporation potential may  be reduced to a daily  average

 level by using the Hamon  Equation (Ha61)


                                 Ep = Nr2s                              (A-7)


 where


     N    =  coefficient  of  daily evaporation  potential

     r    =  duration of  daylight in 12-hour unit/day

     s     =  saturated absolute humidity corresponding to the daily  average
             temperature


Equation  (A-7)  is used to calculate  the  evaporation potential  which is the

upper  bound of  the  evaporation  rate.
                                   A-8

-------
     Overland Flow System  -  It  is  well  known  that  the local  and convective


acceleration terms in Equation  (A-l)  govern the  wave  form and the celerity


of  flood  waves.    Kicftikawa   (Ki59)   indicated   that   these  terms  are


predominated by the  friction term and suggested that  they may be ignored.


This conclusion  was also  confirmed  by  Takasao and  Kishimoto  (Ta61)  and


Ishihara and Takasao (Is62) of overland flow systems through  laboratory and


field  observations.   Takasao  further simplified  the system  equations  by


replacing the  space dependent  depth  of flow h  by an average  flow  depth.


After this modification, Equations (A-l) and (A-2)  become
and
Qo =
                                        H5/3
                      (A-8)
                                            _ Qo
                      (A-9)
where



     Q0   =  rate of overland flow per unit width of trench cover


     H    =  average depth of overland flow over the entire trench cover


     L    =  length of slope (or half of trench width)



     Furthermore, it is assumed that the rate of evaporation from the total


infiltration system will  be  preferentially  obtained  from  the overland flow


system, then the component of evaporation rate may be written as


                                        H
                           ED  when P + — > ED
                            K           At    v



                           P + —  when Ep > P + — > 0
                                \f
At
                     (A-10)
                           0  when P + — = 0
                                       At
                                   A-9

-------
where


     E0   =  component of evaporation rate contributed by the overland flow
             system


     On the  other hand,  since the  maximum rate  of  percolation  from the

overland flow system cannot exceed the  saturated  hydraulic conductivity of

the trench cap,  the percolation rate  can be written as


                   Ks  when P  - E0 +  — > Ks
                                     At
q0
                   P - E0 +JL  when  Ks  > P  - E0 + JL > 0            (A-ll)


                   0  when P - E0 +  - = 0
     The above expressions show that there are four equations available for

solving the  four  dependent  variables, Q0,  H,  E0,  and q0.   Therefore, the

system can be solved independently.


     Subsurface Flow  System  -  For  the purpose  of transforming  the  space

dependent variables into  space  independent variables, the moisture contained

in the  system may be divded  into  three  components:   gravity,  pellicular,

and hygroscopic waters.   Gravity water is the  moisture in a soil  which can

be drained  by gravity force;  pellicular  water is  the moisture  in  a  soil

which cannot  be drained by gravity  force  but  can  be lost to the atmosphere

through natural  evaporation;  and hygroscopic  water is the  moisture  which

will  never be lost through the above natural  processes.  Furthermore, it is

assumed that soil  wetness can  be mathematically approximated by a step-wise

distribution  composed  of  these three components.    Figure  A-l shows  a

comparison  of the  step-wise   wetness  distribution  and   its  corresponding

original  wetness  distribution.


                                    A- 10

-------
                WETNESS
                                TOP OF TRENCH CAP
                                                  GRAVITY WATER DEFICIT
                          PELLICULAR WATER DEFICIT
        STEP-WISE WETNESS
        DISTRIBUTION CURVE
                              BOTTOM OF TRENCH CAP

^ -^^
COMPONENT
FOR HYGROSCOPIC WATER
COMPONENT
FOR GRAVITY WATER
COMPONENT OF POROSITY
 FOR PELLICULAR WATER
                                                             RAE-102213
    FIGURE A-l.   COMPARISON OF A SCHEMATIC NATURAL  WETNESS DISTRIBUTION
                  CURVE  AND ITS CORRESPONDING STEP-WISE  WETNESS DISTRI-
                  BUTION CURVE.
                                    A-ll

-------
     Based  on  the  above concept,  the dependent variables  appearing  in the

 basic differential  equations may be divided into three components, i.e.,
                             VI = Wi + W2 + W3

                 and       q = qi +
where
     W^   =  component of wetness for the hygroscopic water

     W2   =  component of wetness for the pellicular water

     W3   -  component of wetness for the gravity water

     q^   =  component of flux for the hygroscopic water

     q2   =  component of flux for the pellicular water

     q3   =  component of flux for the gravity  water

     qt   =  flux of moisture being transformed from gravity  water to
             pel 1 icul ar water


Substituting Equation (A-12)  into Equations  (A-3)  and (A-4) gives
                           q3 = -DL(W)3  +  K(W)
                                       9 z

                                K(W)  =  0, when W3  =  0


                      and        _M3  .  .  8(q3-
                                 at           az


for the component  of gravity  water and
                      q2 =  -DL(W)_     +  K(w)  _ bD
                                 az               az                      '

                           K(W)  > 0  when W3  > 0

                 and        aW2  = _
                           ot
for the component  of  pellicular  water.


                                   A-12

-------
      Applying the step-wise wetness distribution concept to the above  system
 equations,  Equations  (A-13) and  (A-14) may be  rewritten  by  substituting the
 proper difference forms  of the dependent variables.  The  result  is
                              0    when Zg = Zmax
     and                  tla
                          ^-   -  (qi  -%
where
     q-j   =  flux of moisture infiltrating into the trench
     Ks   =  saturated hydraulic conductivity of the soil
     Zg   =  deficit of gravity water
     ^max =  maximum of deficit of gravity water (equivalent to the
             thickness of the trench cover)
     Wq   =  component of wetness for the gravity water under a fully
             saturated conditions and is numerically identical to the
             porosity for the gravity water

     To simplify the solution of Equation (A-15), the component of moisture
flux for  the pellicular  water,  q2» is  computed based  on  the assumptions
that (1) the flow is predominated by liquid phase transport or (2) the flow
is  predominated by  vapor  phase transport.    The  moisture  flux for  the
pellicular  water  at  any  instant  is  then  chosen  from,  the larger  flux
calculated from the above two assumptions.

     When the flow  is  predominated  by  a  liquid  phase  transport,  the third
term in Equation (A-15) vanishes.   Substituting  the proper difference form
of the  dependent variables gives
                                    A-13

-------
                            qL = -DeWp/Zp + Ke

                     and  -    qL < Ep - E0
where
     qi_   =  flux of pellicular water transported in the liquid phase

     Wp   =  component of wetness for the pellicular water under fully
             saturated condition and is numerically identical  to the
             porosity for pellicular water

     Zp   =  deficit of the pellicular water

     De   =  hydraulic diffusivity at equivalent wetness

     Ke   =  hydraulic conductivity at equivalent wetness


The equivalent wetness for the purpose of this  study is calculated by


                               We = Wh + SWp                         (A-20)


where


     W^   =  component of wetness for the hygroscopic water under fully
             saturated condition and is numerically identical  to the
             porosity for hygroscopic water

     S    =  coefficient  of equivalent wetness  for pellicular  water which
             should  be greater than 0.5 and  smaller than 1.0


     When the flow is predominated by  vapor phase  transport,  the first and

second terms on  the  righthand  side of Equation (A-15) disappear.  Substitut-

ing the proper difference form of the  dependent  variables,  Equation (A-15)

becomes


                           qv  = -bDv(Cs - C0)/Zp                     (A-21)
                                    A-14

-------
where


     qv    =  flux of moisture  being transported in the vapor phase

     Dv    =  diffusivity of water vapor in the trench cap

     Zp    =  deficit of pellicular water

     Cs    =  water vapor concentration at the front of pellicular water

     C0    =  water vapor concentrations at the top of trench cover


     The  diffusion  of  water vapor from the  top of  the  trench  cover to the

atmosphere can be written based on Pick's Law as


                           qv  = -bDa(co - Ca)/Tb                     (A-22)


where

       i
     qv    =  flux of water vapor in the boundary layer of diffusion

     Da    =  diffusivity of vapor in the boundary  layer

     TI-,    =  equivalent thickness of boundary layer

     Ca    =  water vapor concentration in the atmosphere outside the
             boundary layer


     Since the  vapor flux  in  the trench cover and  in the  boundary  layer

should be  identical, Equations (A-21) and (A-22) may be combined to yield


                          „  = . bDa(cs - Co)/Tb
                                   1 +  a
                                                                     (A-23)
                                       TbDv
Furthermore,  the  ratio  of  diffusivities,  Da/Dv,  may   be  obtained  from

Penman's (Pe40) study on the diffusion  of  vapor  through  a porous solid and

Rohwer's  (Ro31)   study   on   evaporation  potentials.    Substituting  their

results  into  Equation  (A-23)  and   replacing   the   numerator   with  the

evaporation potential  yields


                                   A-15

-------
                                  1  +  0.6V         Z                    (A_24)
                                    T^0.66(Wp  +  Wg)
      For the  purpose  of  this  study,  the  coefficient,  (l+O.eVy)/!^,  is
 assumed  to  be  a  constant  and  equal  to  0.5m~^  (see  section  on  Model
 Testing).   When  this  coefficient  is used, Equation  (A-24) becomes
                                 0.66(Wp + Wg)
                                                                      (A-25)
      Now,  the flux  of  moisture being  lost  through evaporation  qp  can be
 computed by

                           qp = -Max( | qL  , | qv | )                  (A-26)

 where  the  Max function implies the  selection of the  largest number among
 those  values designated in the parentheses.

     Again,  by  substituting  the  proper difference  form of  the  dependent
 variables, Equation (A-16) becomes

                          dZp/dt = -(qp + qt)/Wp                     (A-27)

where q^ may be computed by

                               ' q0  when Zp > 0
                                0  when Zp = 0
                                                                     (A-28)
     Equations (A-8 through  A-10),  (A-ll),  (A-17 through  A-19),  and (A-25
through A-28) are the  basic equations for the  practical  infiltration model.
There  are  eleven equations  and  eleven dependent  variables in the system
                                   A-16

-------
equations.   Since  all  of the dependent variables  are  space  independent and



each  pair  of momentum and  continuity  equations can be  solved  in  sequence,



the  computer coding for the  mathematical  model is greatly  simplified  from



that  of the  original system equations.  A  computer model  has been  developed



for  testing  the proposed  system equations and  for the application of  the



model to the evaluation  of  a  low-level waste  disposal  site.






                                 MODEL TESTING





      The  overland   flow  system  using  Equations  (A-8)  and  (A-9)  as basic



equations, has  been studied  through  laboratory studies and field observa-



tions by Takasao  (Ta61).  They concluded  that  the  space  independent system



equations, as  represented  by Equations (A-8) and  (A-9), can reasonably  be



used  to  characterize  the  nature  of overland  flow  for   flood   routing



purposes.   Since the  primary purpose of  this   study  is  the simulation  of



infiltration rates,  the  proposed overland  flow  system equations are judged



to  be adequate  for the infiltration  model.   Testing  of  the  model  was



therefore  concentrated  on  the  subsurface  flow  system.    To  test  the



subsurface  flow  system  submodel,  three   special  cases with  simplified



boundary conditions were selected.  The results  of  simulation were compared



with  existing  studies  having  the  similar  boundary conditions.   They  are



described in  the following  sections.





     Gravity  Water  Drainage Without  Evaporation - A computer simulation  of



gravity water drainage by  gravitational force without evaporation loss was



conducted by  Hillel  and van Bavel (Hi76a).   This simulation was conducted  by



solving equations similar to  the basic differential equations expressed  in



Equations  (A-3)  and (A-4)  without the term  representing the  vapor phase



transport.   The results  of  simulation  for  a sandy  soil  (1.16 m thick) were
                                    A-17

-------
used to  calculate  the cumulative water volume  being  drained from the  soil



(see Figure A-2).





     By  applying  the  same  boundary  conditions  used  in  Hi lie!   and   van



Bavel's  study  to the model  developed for this  study,  the cumulative water



volume drained  from  the  soil  is simulated and  plotted  in Figure A-2.   The



comparison of  the  two results  indicates  that the  proposed  model  does  not



simulate the time  variation of  the  drainage  precisely,  but the calculation



of the cumulative water volume drained from the soil is reasonably close to



the  results  obtained from  Hillel  and van  Bavel's  simulation.   Since  the



main purpose  of the  simulation described in this  study is to  obtain  the



cumulative volume  of water  infiltrated into  the waste  trench,  the proposed



model simulates the rate of infiltration  with acceptable accuracy.





     Steady State Evaporation  Rate  - The  steady state evaporation rate from



a  clay  soil  system  with   a  relatively   high  groundwater  table has  been



analyzed  by  Ripple  (Ri72).   This   study  analyzed  the evaporation  rate by



solving  the  system equation characterizing  the  water flux  transported in



the subsurface flow system  and  the  vapor  flux diffused  into the atmosphere.



The  results  of  his  analysis  for the groundwater table  at  depths  of 0.6,



0.9, 1.2, and 1.8 meters  are shown  in Figure  A-3.





     By applying similar  parameters  and boundary conditions to  the proposed



model and reorganizing the   results  into the  form corresponding to Ripple's



results,  the  results as  shown  in  Figure A-3.   The results of  simulation



from the  proposed model  fit  reasonably well  with  those  obtained by Ripple.





      The above  evaporation rate was simulated for  a  relatively  shallow



groundwater  table.   Therefore,  the transport of soil moisture  is dominated
                                   A-18

-------
                 ^RESULTS OBTAINED FROM THIS STUDY

           RESULTS INTERPRETED FROM HILLEL AND VAN BAVEL'S STUDY
                         345

                           TIME IN DAYS
8
                                                        RAE-1020125
FIGURE A-2.  COMPARISON OF THE RESULTS OF SIMULATIONS FOR GRAVITY DRAINAGE
            OF A TYPICAL SAND USING THE PROPOSED MODEL AND RESULTS
            INTERPRETED FROM HILLEL AND VAN BAVEL's STUDY.

-------
                   1.00
ro
o
                                                            DEPTH=60 cm
                                                                          DEPTH = 90 cm
DEPTH =120 cm
                                                                    DEPTH =180 cm
                              RESULTS OBTAINED BY RIPPLE

                         -'	RESULTS OBTAINED BY THIS STUDY
                               .1       .2       .3       .4      .5       .6


                                    EVAPORATION POTENTIAL (cm/day)
                                                                                RAE-102209
                     FIGURE A-3.  COMPARISON OF THE RESULTS OF SIMULATION FOR THE STEADY STATE

                                EVAPORATION OF CHINO CLAY BY USING THE PROPOSED MODEL AND THAT

                                OBTAINED BY RIPPLE.

-------
by  liquid phase  transport.   However,  when  the groundwater  table is  very



deep,  the steady state  rate  of evaporation may be  dominated by the vapor



phase  transport.   The  computation of  vapor  transport  in  Equation  (A-25)



becomes important under this condition.





     Vapor Phase Transport - There are no data available for  evaluating the



transport of  pellicular  water  in  a vapor phase.   To compare  the character-



istics  of vapor  phase  transport  and  liquid  phase transport,  the flux of



moisture  being  transported by  these  two phases  are computed  for various



depths  of pellicular  water deficit based on Equations  (A-19),  (A-25),  and



(A-26), using evaporation  potentials  of 0.3 and 0.6  cm/d.   The results of



analysis  for  both  sandy  and  clay  soils  are  plotted  and  presented  in



Figure A-4.   The coefficient  represented by  (l.+0.6Vw)/T|j  as  0.5m"-'-  was



selected to obtain the best transition from liquid  phase transport to vapor



phase  transport  for  both  soils  and  for  the  evaporation  potentials  which



ranged from 0.3 to 0.6 cm/d.  The trend of pellicular water flux variations



with the  increase in  the  pellicular water deficit  agrees,  in general, with



the trend described by Philip (Ph74).





           APPLICATION OF MODEL TO AN ACTUAL WASTE  DISPOSAL SITE





     The  low-level  radioactive waste disposal  site  located at  Barnwell,



South Carolina,  was selected  for  an  application of  the model to an actual



waste disposal site.   The trench cover  is constructed  in  two soil layers,



loamy sand  (120  cm  thick) at  the top and  clay  soil (80 cm  thick) at  the



bottom.   First,  the  analysis  simulated  the  infiltration  rates for  a



homogeneous  trench cover for each of the soil  types constituting the trench



cover;  then, the  rate of  infiltration for the  composite trench section was



interpreted  from the results.
                                   A-21

-------
                         SANDY SOIL
                                EVAPORATION POTENTIAL = 0.6 cm/day

                              EVAPORATION POTENTIAL = 0.3 cm/day
                      EVAPORATION RATE USED IN THE MODEL
                   	EVAPORATION RATE TRANSPORTED IN LK3UD PHASE
                 	EVAPORATION RATE TRANSPORTED IN VAPOR PHASE
                         i        I         I         i
                        .2        .3       .4        .5

                   RATE OF EVAPORATION (cm/day)
= ~  1
   O
   sg
   I
    <
                          CLAY SOIL
                                                7
                            EVAPORATION POTENTIAL = 0.6 cm/day

                          EVAPORATION POTENTIAL = 0.3 cm/day
                      EVAPORATION RATE USED IN THE MODEL
                 	EVAPORATION RATE TRANSPORTED IN UQUD PHASE
                 	EVAPORATION RATE TRANSPORTED IN VAPOR PHASE
                 	I	i	I	   i
                        .2
                             .3
.4
.5
.6
                   RATE OF EVAPORATION (cm/day)
                                                   RAE-102124
FIGURE A-4.  TRANSITION  IN  PELLICULAR WATER TRANSPORT  FROM
             LIQUID PHASE TO  VAPOR PHASE CALCULATED  FROM
             EQNS. A.19, A.25,  AND A.26 FOR SANDY AND
             CLAY SOILS.
                             A-22

-------
      The  soil  characteristics for both  layers  were interpreted from  basic



data  reported  by Chem-Nuclear Systems,  Inc.  (CNS80),  and the results  used



for the computer simulation are listed in Table A-l.





      Using the  annual  rainfall  of 118 cm/yr  and  the rainfall distribution



pattern observed in Augusta,  Georgia,  the simulation was conducted for the



loamy  sand  and  the  clay  soil.   The  results of simulation,  presented in



Figure A-5, indicate that the infiltration rates are 45 cm/yr for the  loamy



sand  and  7  cm/yr for  the  clay  soil.   It  is  obvious  that the  rate of



infiltration will  not be  affected  by the  soil  characteristics  below the



level of annual maximum deficit for pellicular water plus the allowance for



gravity water  storage.   The  pellicular water deficit  simulated  for the



loamy sand (Figure A-6) indicated that the maximum pellicular water deficit



reached the  level  of  approximately  50  cm which  is  far  above the  upper



boundary  of  the clay  soil  layer (120  cm  below the  top of trench  cap).



Thus, one may conclude that the  infiltration  rate  for the Barnwell  site is



controlled  by   characteristics   of   the  top  layer,  and   the   rate  of



infiltration  is 45 cm/yr or 17.7 in/yr.





     The above analyses assumed a uniform rainfall  distribution  within the



hourly  period  when  the  rainfall was   recorded.    However,  the  rainfall



distribution  within any hour in a real  case is not necessarily uniform.  By



assuming a peak  factor of  two,   i.e., all  of the  rainfall  being  recorded



hourly is  assumed  to be  concentrated  in the second half of the  recorded



period,  and  reapplying  the same  input  data  to  the infiltration model  to



rerun the  case for the loamy  sand (top  layer),  the  rate of infiltration is



35 cm/yr or 13.8 in/yr.  Therefore, the  infiltration rate for the Barnwell



site  may  vary  between  13.8 and  17.7  in/yr  due  to the  nonuniform hourly



rainfall distribution.
                                   A-23

-------
                                                        TABLE A-l

                                     SOIL CHARACTERISTICS OF THE TRENCH COVER USED IN
                                       SIMULATING THE ANNUAL RAINFALL INFILTRATION,
                                        BARNWELL, RADIOACTIVE WASTE DISPOSAL SITE
ro
Type
Top Layer
Loamy Sand
Saturated
Hydraulic
Conductivity
(m/hr)
0.02
Equivalent
Upward
Diffusivity
(m2/hr)
0.02xlO-2
Equivalent
Upward
Conductivity
(m/hr)
0. 12xlO-5
Porosity
Total
0.51
Porosity
Pellicular
Water
0.24
Porosity
Gravity
Water
0.25
               Bottom Layer
               Clay Soil
0.005
0.13x10
                                                       -3
O.OlxlO-4      0.54
0.44
0.08

-------
 . o 150
    100
     50

  ui
                       LOAMY SAND (Top Layer)
          TOP LAYER: LOAMY SAND, kma =2.0 cm/hr
                              max
                              567


                              TIME (Months)
8    9    10    11    12
    150
Bfz
o o

il
-fjj 100
DC


UJ
     50
                         CLAY (Bottom Layer)
        BOTTOM LAYER: CLAY. kmax = 0.5 cm/hr
>   °
LU    0
                           4567


                                TIME (Months)
8    9    10    11    12
                                                            RAE-102121
      FIGURE A-5.  THE RESULTS OF SIMULATIONS USING THE PROPOSED  MODEL FOR

                 LOAMY SAND AND CLAY SOIL, BARNWELL, S.C., RADIOACTIVE

                 WASTE DISPOSAL SITE.
                                  A-25

-------
ro
01
               E
               o
              ^x
           Sit
 0


50
            2 uj  ioo
                  1KPI
            O. LU  150
              H
              <
                  200
                      0
                                  BOUNDARY OF TOP AND BOTTOM  LAYERS
                            45678

                                 TIME (months)
10    11    12
                                                                                       RAE-102210
                  FIGURE  A-6.  THE RESULTS OF SIMULATING THE VARIATION OF PELLICULAR WATER DEFICIT,
                              LOAMY SAND, BARNWELL, S.C.  RADIOACTIVE WASTE DISPOSAL SITE.

-------
     Independent studies  have  been conducted  by  the U.S.  NRC  (NRC82) and



the  U.S.  Geological  Survey  on  the rate  of infiltration  for  the Barnwell



site,  based  on  an  analysis of  groundwater being  discharged to  a nearby



creek.  NRC's analysis indicated a rate of  14 in/yr;  USGS's,  14 to 17 in/yr.



The  results  of simulation  using  the  infiltration  model   are  in  agreement



with these two studies.






                                 CONCLUSIONS





     1.   The space-dependent variables in the momentum and continuity



          equations  of a  subsurface flow system can be transformed into



          space-independent variables by breaking down the soil moisture



          into gravity water, pellicular water,  and  hygroscopic  water



          components.





     2.   The results of  transformations for the overland  flow system,



          the  subsurface  flow system,  and the atmospheric  diffusion



          system have greatly simplified the  computational procedures



          for simulating  these  systems  and  have improved the stability



          and efficiency  of the  numerical  analysis.





     3.   Although the  transformed system equations cannot simulate the



          dynamic response of soil moisture as precisely  as the original



          partial differential equations,  the  derived system equations



          can be  used to simulate the long-term infiltration rates with



          reasonable  accuracy.





     4.   When  the model  was  applied to the Barnwell  radioactive  waste



          disposal  site,  the results of simulation fit  very  well  with



          the  results  of  analysis  conducted  by  other investigators
                                    A-27

-------
     using the  other methods.  This fact implies that the proposed



     model  can  be employed to simulate the  infiltration  of  rain-



     water through  the cap of  a  waste disposal  trench.





5.    The proposed  practical  infiltration model  is suitable  for



     integrating  into a  larger  system model for  risk  assessment



     of  a  low-level  radioactive  waste disposal  site.
                             A-28

-------
                            APPENDIX A REFERENCES
Ak81   Akan, A. S. and B. C.  Yen,  "Mathematical Model of  Shallow Water Flow
       over Porous Media," J. of Hydr. Div., ASCE HY4, April  1981.

Bi66   Bird, R. B., W. E. Stewart  and E. W. Lightfoot, Transport Phenomena,
       Seventh Edition, John  Wiley and Sons, Inc., New York,  1966.

Ca86   Cahill, J., "Movement  of Radionuclides in Unconsolidated Burial Site
       Near Barnwell, South Carolina," (in press).

CNS80  Chem-Nuclear  Systems,  Inc.,  Environmental  Assessment  for  Barnwell
       Low-Level Radioactive  Waste Disposal Facility, Chem-Nuclear Systems,
       Inc., Columbia, South  Carolina, 1980.

Cr66   Crawford, N. H., and R. K.  Linsley, Digital Simulation in Hydrology:
       Stanford Watershed Model  IV,  Technical  Report No.  39  (Department of
       Civil Engineering, Stanford University, Stanford,  California), 1966.

Cu61   Currie,  J.  A.,  "Gaseous  Diffusion  in  Porous Media,  Part  3  -  Wet
       Granular Material," Brit. J. Appl. Phys. 12,  275-281,  1966.

Fo68   Foster, G.,  L.  Huggins,  and L. Meyer,  "Simulation of  Overland Flow
       on  Short  Field  Plots,"  Water  Resources  Research,  Vol.  4,  No.  6,
       1968.

Ha61   Hamon, W. R.,  "Estimating Potential  Evapotranspiration,"  ASCE, HY3,
       1961.

Hi76a  Hillel, D. and C. Van  Bavel, "Simulation of Profile Water Storage as
       Related to  Soil  Hydraulic  Properties,"  J. Soil  Science  Society  of
       America, Vol. 40, No.  6, November 1976.

Hi76b  Hi lie!,  D.,  "On  the   Role  of  Soil  Moisture  Hysteresis  in  the
       Suspension  of  Evaporation  from  Bare  Soil  Under   Diurnally  Cyclic
       Evaporativity," Soil  Science, 122, 6, 1976.

Hi80   Hillel, D.,  Fundamentals  of  Soil   Physics,   pp.  221-223,  Pergammon
       Press,  New York,  1980.

Hj81   Hjelmfelt, A.,  "Overland Flow Time Distributed Rainfall," Journal  of
       Hydraulic Division, ASCE, February 1981.

Hu77   Hung, C. Y.  and C. J.  Keifer,  "Storm Runoff Simulation for the Lake
       Diversion Area,"  a report  prepared  for the  Illinois  Department  of
       Transportation, Division of Water  Resource, February 1977.

Hu83   Hung, C. Y., G. L. Meyer,  and  V.  C.  Rogers,  Use of PRESTO-EPA Model
       in Assessing  Health  Effects  from  Land Disposal  of LLW  to Support
       EPA's Environmental Standards:  U.S.  Department  of Energy,  Proceed-
       ings of 5th  Annual  Participants' Information Meeting on DOE Low-Level
       Waste  Management  Program,   Denver,   Colorado,   August  30,   1983,
       CONF-8308106,  Idaho Falls, Idaho.
                                   A-29

-------
 Is62    Ishihara, T.  and  T.  Takasao, "A  Study  on the Subsurface Runoff  and
        Its Effects on Runoff Process," Trans JSCE No. 79,  1962.

 Is63    Ishihara, T.  and  T.  Takasao,  "A Study on the Runoff  Pattern  and  Its
        Characteristics" Bull. Disaster Prev. Research Inst., Japan,  No.  65,
        1963.

 Iw64    Iwasa,  Y.,  "Fundamental  Principles  of Open-Channel Flow," published
        by Hydraulic Committee, Japan Society of Civil Engineers, 1964.

 Ki59    Kichikawa, H., "A Study on the Underground Flood Control Reservoir,"
        Proceedings, JSCE, 1959.

 Mo71    Moore,  W. L.  and  B.  J. Claborn,  "Numerical  Simulation  of Watershed
        Hydrology,"  in proceedings of the First Bilateral U.S.-Japan Seminar
        in Hydrology, January 1971.

 Pe40    Penman,  H.   L.,   "Gas  and  Vapor  Movement  in  the  Soil:    I,  the
        Diffusion of  Vapor  Through Porous Solids,"  Journal,  Agr.  Sci., 30,
        pp. 437-461, 1940.

 Ph74    Philip,  J.  R.,  "Water  Movement  in Soil,"   pp.  29-47.   Ed.  D.  A.
        De Varies and N.  H.  Afgan, Halsted Press-Wiley,  New York, 1974.

 Ri72    Ripple, C. C., J.  Rubin, and T. Van Hylkama, "Estimating Steady-State
        Evaporation  Rate from Bare Soil Under Conditions of High Water Table,"
        U.S. Geological  Survey,  Water Supply,  pp. 2019-A, 1972.

Ro31   Rohwer, C.,  "Evaporation from a  Free Water Surface," U.S. Department
       of Agriculture,  Tech. Bull. 271, 1931.

Ta61   Takasao, T.  and S.  Kishimoto,  "An Experimental  Study on  the  Runoff
       of Rainfall," Bull., Disaster Prev.  Research  Inst.,  Japan,  No.  4,
        1961.

NRC82  U.S. Nuclear Regulatory  Commission,  Environmental  Assessment  for the
       Barnwell Low-Level Waste  Disposal Facilities, NUREG-0879,  Division
       of Waste Management,  1982.
                                   A-30

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                  APPENDIX B
  AN OPTIMUM GROUNDWATER TRANSPORT MODEL FOR
APPLICATION TO THE ASSESSMENT OF HEALTH EFFECTS
  DUE TO LAND DISPOSAL OF RADIOACTIVE WASTES

-------
                                APPENDIX B






     This  appendix  presents  background  and  theory  for  the  groundwater



transport model  and  DDETA correction factor  used  by  the  MAIN  routine and



VERHOR subroutine  in  the  PRESTO-EPA-POP  code.  The  model  was developed by



Hung and the original  publication  is  included  here.
                                      5-2

-------
 NLCI.EAR ANDCHKMICAL WASTK MANACEMKST. Vol. 6, pp. 41-50, 1986
 Printed m [he USA. All nghls reserved.
 AN OPTIMUM GROUNDWATER TRANSPORT MODEL
 FOR APPLICATION TO  THE  ASSESSMENT OF
 HEALTH  EFFECTS  DUE TO LAND  DISPOSAL
 OF  RADIOACTIVE  WASTES

 Cheng Y. Hung
 Office of Radiation Programs, U.S. Environmental Protection Agency, Washington, D.C. 20460
ABSTRACT. This paper presents a groundwater transport model for simulating radionuclide transport in an aquifer, using
an approximate solution of the basic transport equation. The model is designed to avoid (1) relatively high computer simula-
tion costs normally experienced in numerical models and (2) the large errors sometimes introduced when the physical boun-
dary conditions are converted to a mathematical form  suitable for the analytical model. The model neglects initially the
effect of radionuclide transport through dispersion and compensates for this effect subsequently with a health effects correc-
tion factor. This correction factor is found to be a function of the Peclet number, a dimensionless parameter expressing the
relative importance of diffusion and convective transportation, and the "transport number," which has been defined and
can be determined by using the parameters of the groundwater transport system. The model has a low cost of simulation and
yet maintains reasonable accuracy of predicting the cumulative radionuclide flowing through a section. This is the primary
output expected from a groundwater transport model for health effects assessments. The model has been integrated into the
PRESTO —EPA model designed for the prediction  of radiation effects due to a shallow-trench operation.
 INTRODUCTION

 Comprehensive studies on the evaluation of an op-
 timum method  of diposing radioactive wastes  have
 been  conducted by  various government agencies
 (1,2) and by an Interagency Review Group (3). All of
 these  studies have unanimously  concluded that the
 geological disposal method is one of the most viable
 alternatives. Because  the transport of radionuclides
 through an aquifer to the biosphere is a primary
 pathway, the groundwater transport model, which
 simulates  the  migration  of radionuclides  in an
 aquifer, becomes one of the important submodels re-
 quired in a health effects assessment model.
   To date, there  are more than 108 groundwater
 transport models (4) available. However, some of the
 models fail to consider the process of  radionuclide
 decay and/or sorption and, therefore, are not  suit-
 able for the assessment  of a  radioactive waste dis-
 posal site. The rest of the models, which may be  suit-
RECEIVED 12/24/84; ACCEPTED 12/6/85.
   Acknowledgements — The author is grateful to Mr. G. Lewis
Meyer of EPA for his valuable suggestions and continuous en-
couragement throughout the development of this model. Special
acknowledgements should be made to Dr. Akio Ogata of USGS
and Professor Donald S. Cohen of the California Institute of
Technology for their suggestions and criticisms during the course
of model review.
  able for health effects evaluation, can be subdivided
  into two groups: the analytical model and the nu-
  merical  model.  In  general,  the  application of  an
  analytical model is limited by its specific form  of
  boundary conditions. Therefore,  when the actual
  boundary conditions do not match the form that the
  model called for, some approximation of its actual
  boundary conditions would be required before the
  analytical solution  could  be  applied.  As  a result,
  these models may suffer from considerable error due
  to the approximation of boundary conditions.
    The application of a numerical model generally re-
  quires many more  tedious computations  than the
  analytical approach. For example, the accuracy  of
  simulation depends greatly on the adjustments  of
  time and space increments; severe errors may result if
  they are improperly adjusted.  On the other hand, a
  proper adjustment of these increments may result in
  consuming excessive computer time for the simula-
  tion, in some cases. Therefore it is conceivable that
  the cost of simulation may become prohibitive when
  the model is applied to long-term simulations such as
  health effect evaluations.
    The basic groundwater transport model aiming for
  health effects assessment was developed by Hung (8)
  and was integrated  into the PRESTO-EPA model
  (9), a  model to  predict  the radiation effects from

B-3

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42
                                                                                         C. Y. HUNG
shallow trench operation. Since then, the same model
has been improved in theoretical background and in
practical application.
   The purpose of this paper is to present the ground-
water transport  model used in the PRESTO-EPA
model and its characteristics.
 APPLICATION OF EXISTING MODEL IN
 HEALTH EFFECTS EVALUATION
 The basic  equations for  a groundwater  transport
 system include the momentum, the energy, and the
 continuity equations for the hydrodynamic system
 and for the solute. Using tensor notations, the equa-
 tions take the form (10)
                                          (1)
    [(Qk/ti)H(Vp - QgVz)} + V • p* • VT - qL
         = (d/dt)[neU + (1  - n)(QCpT)]     (2)
   v = -(k/n)(Vp - QgVz)
   V
   Vey_ + cf = -(d/dt)(no)
V . [QC(k//j.)(Vp -
  - q-C - Qn\dRC = (d/dt)(enRC),
                                        VC
                                           (3)
                                             (4)
in which C is the concentration of the radionuclide in
the fluid  phase; y_  is the velocity vector; k  is the
permeability; jj. is the viscosity of the fluid; p is the
pressure; Q is the mass density; g is the gravitational
acceleration; D is the dispersivity tensor; Tis the tem-
perature; qL is the rate of heat loss; H is the fluid en-
thalpy;  n is the porosity;  z is the height above refer-
ence plane; \d is the radionuclide decay constant; R is
the retardation factor; U is the internal energy; cp is
the specific  heat; q' is the rate of fluid withdrawal;
and subscripts h and c are the heat energy and com-
ponent of mass,  respectively.
   The preceding non-linear equations  characterize
the transport of  radionuclides in a groundwater sys-
tem. Since each of  the preceding equations are re-
lated through dependent variables, the direct solution
of the system equation for any boundary and  initial
conditions is extremely difficult. A commonly used
practice in solving the system equation is to assume
that the flow of groundwater is steady and that there
is no heat energy being generated or absorbed  in the
system.  The  system equation then reduces to a single
equation:
   R(dC/d() - V • (D « VC) + VVC
            + X,/?C = O,
                                          (5)
in which V is the interstitial velocity ( V =  V/AJ).
Equation 9 has been further simplified and solved by
numerous investigators (10,11,12, and 13) employing
numerical or analytical approaches.  However, some
difficulties  are often encountered  in applying these
models for  health effects assessments. They are de-
scribed in the following sections.
Numerical Models
The existing multidimensional  models are  solved
either by the finite-difference method (10) or by the
finite-element method (11,12,  and  13).  A  model
employing the finite-element  method is, in general,
found to  be more efficient than one employing the
finite-difference method (12). However, the time re-
quired to  execute a computer model employing the
finite-element method is still  far beyond the  limita-
tions of a normal project budget for  risk assessment
when numerous cases with long durations of simula-
tion must be considered.

Analytical Models
Lester,  Jansen, and Burkholder (6)  developed an
analytical groundwater transport model for  a  one-
dimensional, semi-finite aquifer system having im-
pulse release and  decaying band release  boundary
conditions. These boundary conditions at x =  0 were
expressed  as
   C = C06(t)
and
   C= (C0/Oexp(-Xdt)
                                                                                                 (6)
                                                                                                 (7)
for the impulse release and the decaying band release,
respectively. In the preceding equation, x is the space
coordinate,  t is  the time, td is the duration  of ra-
dionuclide leaching, and C0 is the concentration of
radionuclides at  t — 0.
   Ford,  Bacon,  and Davis, Inc. employed an ana-
lytical model that assumed that the rate of radionu-
clide release at  any time is proportional to the in-
ventory of  radionuclides remaining  at the source
point (7). Mathematically, it is expressed as
   C = (Xi/m/Q JExp[ - (Xd + \L)t],              (8)

in which  Xi is the leaching constant,  lm is the initial
inventory of the radionuclides in the waste depository,
and Q, is the rate of groundwater flow.
   These  analytical models  have made considerable
contributions in  groundwater transport modeling by
simplifying the simulation procedures. However, the
application of these models to health effects assess-
ments is limited, because it requires the approxima-
tion of converting the actual boundary condition to a
form meeting the requirements  of  the analytical
model. This may result in considerable simulation er-
ror in some cases.
   The preceding  discussion   implies that  existing
numerical and analytical groundwater models  may
either be too costly  to compute or  may introduce
large errors when applied  to health effect assess-
ments. Therefore,  a  more  accurate  and  more  eco-
nomic groundwater transport model has been devel-
oped for  health risk assessments and is presented in
this paper.
                                               B-4

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 AN OPTIMUM GROUNDWATER TRANSPORT MODEL
                                                    43
 THEORETICAL BACKGROUND OF THE
 OPTIMUM GROUNDWATER TRANSPORT
 MODEL FOR HEALTH EFFECTS
 ASSESSMENTS

 Derivation of Basic Equation
   The groundwater transport  model to be discussed
 in this  section simulates  the transport of  radionu-
 clides  from  a disposal  site to a point where  ra-
 dionuclides are pumped  out  to the  biosphere  for
 human uptake or discharged  into a surface stream
 for another mode of transportation. To simplify the
 model,  it is assumed that the flow of the fluid carry-
 ing the radionuclides is  steady, uniform, and one-
 dimensional. It is also assumed that the dissolved ra-
 dionuclides are in equilibrium with those adsorbed by
 the solids in the aquifer formation and that decay is
 in progress for both dissolved and absorbed radionu-
 clides.
   The basic one-dimensional groundwater transport
 equation  for  the model simulating  radionuclide
 migration in an aquifer may be reduced from Eq. 5 to
   D(32C/dx2) -  V(3C/3x) - R(dC/dt)
              -  \,RC = 0
(9)
 which is to be solved by the following  initial and
 boundary conditions:
   C = 0,       at all x,    when t = 0,       (10)

   C = C0(t),    at x = 0,   when t < 0, and
   C = finite,   at x - oo   when t > 0.
                                             (11)
 For the convenience of analysis, one may transform
 the dependent variable from radionuclide concentra-
 tion,  C, into the rate of radionuclide transport by
 multiplying Eqs. 9,  10, and 1 1 by the rate of ground-
 water flow. When this transformation is completed,
 the preceding equations  become:
   D(d*Q/dx2) -  V(dQ/dx) - R(dQ/dt)
              -  \dRQ =  0                   (12)
   Q = 0,      at all x,     when t =  0,
   Q = Q0(t),  at x = 0,   when t >  0, and   (13)

   Q = finite,  at x -  oo   when / >  0,

 where Q denotes the rate of radionuclide transport.
   Since Eq. 13 is an undefined boundary condition,
 the analytical solution for Eq. 12 cannot be obtained.
 However, one may express its solution into a con-
 volution form expressed by:
          \'0Qo(t ~ r)u(r)dr,                   (14)
in which u denotes the radionuclide release rate at the
discharge end and, x = L, which responds to the unit
release of a radionuclide at x = 0 and when T  = 0.
This function  is normally known as unit response
function.
         The preceding unit response  function,  U(T), has
       been thoroughly studied by Burkholder et al. (6),
       with the following results:
         u(T) = (Y/2LM(RP/ir03) Exp| -
             -(PO/4R)[(R/6)-l]2\.
                              (15)
       in which P is the Peclet number (= VL/D); 8 is the
       dimensionless time  (=  rV/L);  Nd  is  the  decay
       number (= \dL/V). By substituting Equation 15 into
       Eq.  14, one obtains:
         QW  = U Q.(t -  r) • (V/2L)^f(RP770^)
                    - (P6/4R)[(R/ff) - IVldr.      (16)
         Equation 16 cannot be integrated because Q0(t - T)
       is undefined. However, if the dispersion term, D(d2Q/
       dx2),  in Eq. 12 is  neglected, then the unit response
       function, I/(T), for the modified Eq. 12 becomes (6):
             = Exp(-RL\d/V)8(r - RL/V)
                              (17)
      As a consequence, Eq. 14 can be integrated, and the
      result is
         Q'(t) = Q°(t ~ RL/V)E\p(-\dRL/V).
                             (18)
       In Eqs. 17 and 18, 5 denotes the delta function, and
       the prime on i/ and Q' denotes variables responding
       to  the system  with  the  dispersion  term  being
       neglected.
         Although Eq. 18 is easier to calculate than Eq. 16,
       the results obtained from Eq.  18 include an error
       resulting from neglecting the dispersion term in the
       basic transport equation. To compensate for this er-
       ror,  a correction factor defined  by
                     = Q(t)/Q'(t)                  (19)
      has been introduced. After this correction factor has
      been characterized, the rate of radionuclide transport
      Q(t) can be obtained  by combining Eq. 18 and 19.
      The result is:
- RL/ K)Exp( - RL\d/ V).
                                                  (20)
         In Eq. 20, the correction factor £ is expected to be
      a function of  /, P, and \dRL/V; the complexity of
      this  term  prohibits its application. This correction
      factor  is further transformed into time independent
      factor  based on the ground that the trasport model is
      primarily  for  the  purpose of risk  assessment. The
      transformation is derived as  follows:
         The assessment of health effects  due to  direct
      and/or indirect  ingestion of groundwater contami-
      nated with radionuclides involves complicated simu-
      lation of the history of organ doses. Such an assess-
      ment also requires the probabilistic analysis of the
      occurrence of fatal cancer effects following the simu-
      lation of radionuclide transport  in the acquifer. Due
      to the complexity of the dose  and health effects simu-
      lation,  a linear model is generally employed in vari-
                                               B-5

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44
                                                                                           C. Y. HUNG
 ous risk assessment models. An example of this ap-
 plication is the PRESTO-EPA model (9).
   When  a  linear model is  employed, the  annual
 health effects due to the ingestion of a specific ra-
 dionuclide, E,, for a community with a population of
 P' can be expressed by (14):
   (H.), = (P'/T.) £ £.(*/),...
                                          (21)
 in which  R, is the health  risk conversion  factor per
 unit rate  of chronic ingestion, T, is the number of
 years of life expectancy, E is the rate of radionuclide
 exposure, and / and 1  denote the order of radionu-
 clide and human organs.  Furthermore, since a  risk
 assessment involves the estimates of health effects for
 infinite generations residing at the community of in-
 terest, the total health effect due to the exposure  rate
 of E. pCi/yr is calculated by the following generalized
 equation:
(H,), =  \"(P'/T.) - 2J EUR,),,Idt
                   1=1
                 M
     =  (P'/T.) • £ (R/)l,l^E.dt,
                1=1
                                             (22)
 where H, is the total health effects and t is the time.
   Since the annual rate of pumping radionuclides
 that will  be ingested  by humans is directly propor-
 tional to  the rate of radionuclides being transported
 to the wellpoint, one  may write:
   E, = rQJP
                                          (23)
 where r is the ratio  of the rates of radioactivity ex-
 pected to be uptaken by the inhabitants of the com-
 munity to the rate of radioactivity reaching the well-
 point, and Q, is the rate of radionuclides being
 transported to the wellpoint.
   Substituting Eq. 23 to Eq. 22,  one obtains
      ,), = (r/T.)
                                          (24)
Equation 24 indicates that the total health effects de-
pend on the total cumulative activity of radionuclides
reaching the wellpoint and are independent of the
time variation of the transport rate. Therefore, for
the purpose of health effects assessment, the key in-
put required from a groundwater transport model is
the cumulative radionuclides reaching the wellpoint
over an infinite period of time. This is the key con-
cept used  in developing  the groundwater model
presented in this paper.
   Since the  goal  of health effects assessments is
estimating  fatal  health effects, one may also intro-
duce a long-term health effects correction factor, 77,
defined by:
   r, = //,////,                                 (25)
where H, and H,' represent the total health effects ob-
tained from the groundwater pathway at the discharge
end  with and  without considering  the  dispersion
term, respectively.
   For the purpose  of developing a  ground water
transport model, one may assume that the popula-
tion affected by the  well water remain constant and
that the  total health effects  due to the released ra-
dionuclides are so small that they would not alter the
size of the population at risk and the other factors af-
fecting the health effects. If this is the case, there will
be a linear relationship between the  cumulative ra-
dionuclides reached  at that point and the expected
total health effects.  Substituting  Eq.  24 into Eq. 25
and  lumping together all terms  affecting the health
effects conversion factors into a single health effects
conversion factor, then Eq. 25 can be rewritten as:

   r, = ((Fk)\:Q(t)dt}/((Fh-)\:Q'(t)dt}.          (26)

where Fh denotes the conversion factor for health ef-
fect  from cumulative radionuclide release.
   Subsequent  substitution of  Eq. 14 into Eq. 26
yields:
                                                    Q0(t - T)u'(T)dTdt.                         (27)
                                                 When the order of integration of the double integral
                                                 for both numerator and denominator is reversed, Eq.
                                                 27 can be rewritten as:
   r>  - (
   Q0(t -
                                                                                                  (28)
                                                 Furthermore, when the independent variable, t, is
                                                 transformed to a such that a = t — T, Eq. 28 becomes
                                             (29)
   Since Q0 is independent of T and u and u1 are  in-
dependent of a, the double integrals in the denomina-
tor and numerator can now be separated into prod-
ucts of single integrals and yield:
which can be simplied as:

   1  = [\'u
-------
 AN OPTIMUM GROUNDWATER TRANSPORT MODEL
                                                    45
Equation 31 is the basic equation of this groundwater
transport model.


Characterization of Health Effects Correction Factor
To determine the characteristics of the health effects
correction factor, one may first  substitute Eqs. 15
and 17 into Eq. 30 and then complete the integration
of the denominator. This yields
                 -  (PO/4R)(R/6 -
                Exp(-/?LX,/K)
                                        •  (32)
The numerator of Eq. 32 can also be integrated into a
modified Bessel function of the second kind (15);
when the result of integration is substituted, Eq. 32
becomes:
       Exp I —	—
            Exp  -
                                          (33)
          Equation 33 indicates that the health effect correc-
       tion factor is a primary function of the Peclet number
       and the parameter expressed by \dRL/V. This pa-
       rameter represents the ratio of the radioactive decay
       constant, \d,  and  the "transport constant", V/RL,
       and is designated as "transport number"  for  this
       study. The preceding results were plotted on a Peclet
       number vs. transport number plane, as shown in Fig.
       1 .  This figure indicates that the health effects conver-
       sion factor, 7), increases with the increase in transport
       number and decreases with the increase in Peclet
       number. Equation 33 also indicates that the health
       effects correction factor is always greater than  1 .

       Proposed Groundwater Transport Model for
       Health Effects Assessment
       Based on the previous discussions, a groundwater
       system with initial and boundary conditions as shown
       in  Eq. 13 may be simulated by Eq. 31, which is dupli-
       cated as:
         G(0 = 17 • Qo(/
                                                                          • Exp(-RL\d/Y).  (34)
                   10,000
                    8,000
                    6,000

                    4,000
                    2,000
                    1,000
                     800
                     600
                     400
                     200
                £    100
                 |     80
                      60
                      50
                      20
                      10
                                    A
                                      L
 /
LL
        fill   /I/   I
      z
                                               7/
rz
LLUL
77
                  77
                                                            L/LL
LL77/7LI
             7_7
                  LTL
              77
             Z
                          / ,
                                7
                   L'l
                     77
                       0.1   0.2   0.4  0.60.81     2     4  6 8 10    20   40 6080100

                                         Trtniport Number, XdRL/V

                    FIGURE 1.  Results of health effect collection factor analysis, Equation 33.
                                             B-7

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46
                                                                                          C. Y. HUNG
Equation 34  represents an algebraic  equation,  in
which constant, r;, is determined from Eq.  33; and
the terms RL/V and X, are also known constants
determined  from the characteristics  of the ground-
water system.  Therefore,  the proposed  model  de-
scribed by Eq. 34 is the simplest and most economical
to process when it is integrated into  a health effects
assessment model.
   It  should  be noted  that  when  this  model  is
employed in a health effects assessment model, there
may be a slight error in the health effects for each in-
dividual generation, but the total health  effects  for
all generations should remain the same as that ob-
tained from  the direct  integration of Eq. 14. The
nature of this error is characterized in the following
section.
CHARACTERIZATION OF THE POTENTIAL
ERROR OF THE PROPOSED MODEL
Hypothetical Groundwater System
To characterize the nature of error  incurred by the
proposed model, a hypothetical groundwater trans-
port system  was  established.  In the  hypothetical
groundwater system, it was assumed that: the veloc-
ity of groundwater flow is 100 m/yr; the location of
radionuclide  discharge  is  500 meters  downstream
from  the source point where the radionuclide is re-
leased; the coefficient of dispersion is 300 mVyr; the
rate of radionuclide release at the source point, x = 0,
varies with time and is represented by
                           10
                       l

                     II
                     o: —
                     •! i
                     ~ o
                     1*
                                                                                800
                                    Rite o( RelUM »t x • 0
                                    Result of Analysis. Optimum Model
                              ---- Result of Analysis, Ex»ct Model

 FIGURE 2.  Comparison of the results of analyses obtained from the Optimum Model and the Exact Model, Case I, X,, = 0.000693,
 200 years.
                                                   B-8

-------
AN OPTIMUM GROUNDWATER TRANSPORT MODEL
                                                                         47
   Qo(t) = 0
                            for 0 < / < td
for t > td,
                                               (35)
 where td is the duration of radionuclide release.
   Three cases are assumed  for the analysis. Case I
 represents a fast release, td  = 200 yr, and  long  ra-
 dionuclide half-life, X,  = 0.000693.  Case II  repre-
 sents a  fast  release,  td  =  200  yr,  and short  ra-
 dionuclide half-life, X^  = 0.0693.  Case III represents
 a slower release, td = 400 yr, and long radionuclide
 half-life, \d = 0.000693. Each case is also subdivided
into three subcases with the retardation factors equal
to 1, 10, and 100, respectively.

Method and Results of Analysis
Two models were developed for the analysis. One of
them  was developed  on a numerical integration of
Eq. 16 and was designated as the "Exact Model." The
other model was developed based on Eq. 34 and was
designated as the "Optimum Model." Each of these
models was designed to compute  the radionuclide
discharge rate at  the downstream end of the aquifer
and the cumulative radionuclides released at the dis-
charging point over infinite time. The results of com-
                                100
                                        200
                                               300    400     500

                                                    Time, yr
                                         600
                                                                            700
                                                        800
                          Legend:
                          ..... ••— Rate of Release at x - 0
                          ^— — Result of Analysis, Optimum Model
                          - — — — Result of Analysis, Exact Model

FIGURE 3.  Comparison of the Results of analyses obtained from the Optimum Model and the Exact Model Case II, X,, = 0.0693, 1,
200 years.
                                                   B-9

-------
48
                                                                                            C. Y. HUNG
 puter analyses using these two models are presented
 in Figs. 2, 3, and 4.

 DISCUSSION OF RESULTS
 For Cases I and III with long radionuclide half-life,
 the rate of radionuclide release and the cumulative
 radionuclide release computed from the exact model
 and the optimum model agree very well for all three
 subcases assumed. However, the results of the Case
 II analysis, where the radionuclide half-life is short,
 indicate, that the rate of radionuclide discharge ob-
 tained from the optimum model deviates more and
more from that obtained from the exact model as the
retardation factor increases. Nevertheless, the major
deviations are merely in the time-lag of radionuclide
discharge, whereas the peak discharge showed little
deviation (Fig. 3). The results of this latter analysis
also indicated that the above deviation will be miti-
gated for those radionuclides with  longer half-life;
i.e., with smaller  transport number (Fig.  2). Fortu-
nately, a system with larger transport numbers results
in a limited quantity of radionuclide discharge at its
discharging point, as can  be seen by comparing case
II-3 with cases II-2 or II-1. This result implies that the
discharge of radionuclides  under a high transport
                  So
                 O 5
                  • «
                   cc
                   •S
                 fl
                 S i
                 11
                 | c
                 II
                 oc S
                 "H
                 S5
                                                                                   800
                           Legend:

                           	Rate of Release at x • 0
                           ——— Result of Analysis, Optimum Model
                           	 R«ult of Analysis, Exact Modal
FIGURE 4.  Comparison of the results of analyses obtained from the Optimum Model and the Exact Model, Case II, X, = 0 000693 t
400 years.                                                                                '     '      ' '
                                               B-10

-------
AN OPTIMUM GROUNDWATER TRANSPORT MODEL
number, such  as Case II-3, would not be a major
concern from the point of view of health effects as-
sessment.  Besides,  this  deviation should  further
decrease with the increase in the duration of radionu-
clide release at the  radionuclide  source  point,  as
shown in Figs. 2 and 4.
   Nevertheless, the cumulative radioactive discharge,
which is the primary parameter in  determining total
health effects from a radioactive waste disposal site,
remains the same for those obtained from the exact
model and from the optimum model in all cases. This
agreement implies that the proposed optimum ground-
water transport model can be integrated  into the
health effects assessment  model without introducing
any significant error in the assessment of health ef-
fects.
APPLICATION TO A RISK
ASSESSMENT MODEL
The  optimum  groundwater  model has  been  in-
tegrated into the PRESTO-EPA  model, a  model
designed to predict the radiological effects due to the
disposal of radioactive wastes by  a shallow  trench
operation. The  PRESTO-EPA model is a complete
risk assessment  model.  It includes  the simulation of
radionuclide transport  from  the  wastes  through
hydrologic and atmospheric  pathways  to environ-
mental  receptors  and from the environmental  re-
ceptors to human organs through  food-chain path-
ways and the evaluation of fatal health effects from
the  history of organ  dosimetries. The model  was
developed by the Oak Ridge National Laboratory for
EPA.
   The groundwater  transport submodel receives  the
output from the leaching submodel as its boundary
conditions and  calculates  the rate of  radionuclide
transport at the wellpoint. These outputs are then  fed
into the  food-chain  submodels for human exposure
evaluations and,  subsequently,  for health   effects
assessments.
   The PRESTO-EPA model has been used to assess
the health effects for over 400 different combinations
of  radionuclide source terms  with various   hydro-
geological, demographical, and disposal conditions.
The model interacts with other submodels smoothly,
implying  that the proposed optimum groundwater
transport model can be integrated into a risk  assess-
ment model.
CONCLUSION
An optimum groundwater transport model for health
effects assessment has been derived and characterized.
The processing time required to simulate this model
is  significantly less than that for other comparable
models,  because it requires only algebraic calcula-
tions.
   The error from simulating the peak discharge of
radionuclides using the "optimum" model, as com-
pared with the results from that of the "exact" model
(i.e.,  the numerical model  represented by  Eq. 16
and 35), may be noticeable when the  groundwater
transport number is  greater than  5. However, the
cumulative  radionuclides released under  the  same
conditions is normally only  a  small  fraction  of the
cumulative  radionuclides  released  at  the  source
point. Therefore, the effect of this error should not
be as  important as that for  those radionuclides with
lower transport numbers.
   The predicted cumulative radionuclides passing
the point of interest obtained from the proposed "op-
timum" model agree very well with that obtained
from the "exact" model in all cases. This implies that
the proposed model can be integrated into a health
effects assessment model with confidence, if one ac-
cepts a one-dimensional flow model.
   The application of the proposed optimum ground-
water transport model to the PRESTO-EPA model
indicated  that the model interacts with other sub-
models very smoothly, implying that the model can
be easily integrated  into a risk assessment model.
REFERENCES

 1. The Mitre Corporation. Alternative disposal concepts for
   high-level  and  transuranic  radioactive  waste disposal.
   USEPA, ORP/CSD 79-1 (1979).
 2. Ford, Bacon,  & Davis Utah, Inc. Screening of alternative
   methods for the disposal of low-level  radioactive  wastes.
   USNRC, NUREO/CR-0308,  UC 209-02 (1978).
 3. Interagency Review Group. Report to the  President by the
   interagency review  group on nuclear  waste management.
   TID-29442 (March 1979).
 4. Science Applications, Inc. A compilation of models and
   monitoring techniques. USDOE, ORNL/SUB-79/13617/2,
   SAII/3-80-006.
 5. Smith, C.  B.;  D. J. Egan, W. A. Williams, J. M. Gruhlke,
   C. Y. Hung, and B. Serini. Population risks from disposal of
   high-level  radioactive  wastes  in  geological respositories.
   USEPA Report, 520/3-80-006.
 6. Lester, D.  H.;  George Jansen, and H. C. Burkholder. Migra-
   tion of radionuclide chains through an adsorbing medium.
   AICHESymp. Series 71: 202 (1975).
 7. Ford, Bacon, & Davis Utah, Inc. A classification system of
   radioactive waste disposal — what waste goes where. USNRC,
   NUREG-0456, FBDU-224-10 (1978).
 8. Hung, C. Y. An optimum model to predict radionuclide trans-
   port in an aquifer for the application to health effects evalua-
   tions. Proceedings of Inter-Agency Workshop on Modeling
   and Low-Level  Waste  Management,  Denver, Colorado,
   (1980).
 9. U.S. Environmental  Protection Agency. PRESTO-EPA: A
   low-level radioactive waste environmental transport and risk
   assessment code—methodology and user's manual, in press.
10. INTERA Environmental Consultants, Inc. Development of
   radioactive  waste-migration  model,  Sandia Laboratories
   (1976).
                                                    B-ll

-------
50
                                                                                                 C. Y. HUNG
II.  Dugid, J. O. and M.  Reeves.  Material  transport through
    porous media: a finite-element galerkin model. Oak Ridge Na-
    tional Laboratory, ORNL-4929 (1976).
12.  Finder, George  F.  and William G.  Gray,  Finite element
    simulation in surface and subsurface hydrology.  Academic
    Press, New York (1977).
13.  Yen, G. T. and D. S. Ward. FEMWATER: A finite-element
    model of water flow through saturated-unsaturated  porous
    media. Oak Ridge National Laboratory, ORNL-5567 (1980).
14.  Begovich, C. L. et at., DARTAB: A program to combine air-
    borne radionuclide environmental exposure data with dosi-
    metric and  health effect data  to  generate  tabulations of
    predicted health  impacts. Prepared for the  Environmental
    Protection Agency, ORNL-5692, (1981).
15.  Abramowitz, M. and I. A. Segun. Handbook of mathematical
    functions with formulas, graphs,  and mathematics tables. Na-
    tional Bureau of Standards, Applied Matthematics Series No.
    55 (1972).
16.  New York State Geological Survey. Computer modeling of ra-
    dionuclide migration pathway at a  low-level waste burial
    ground. West Valley, New York. USEPA (1980).
17.  Smith, J. M.; T. W. Fowler, and A. S. Goldin. Environmental
    pathway models for evaluating population risks for disposal
    of  high-level radioactive waste in geologic repositories.
    USEPA, 520/5-80-002 (1980).
NOMENCLATURE
 C: concentration of radionuclide disolved in fluid.
C0: concentration of radionuclide at t = 0.
 cf: specific heat  of fluid.
 D: dispersivity of fluid.
 E: rate of radionuclide exposure.
Fk: fatal health effect conversion factor.
 g: acceleration of gravitational force.
 H: enthalpy of fluid.
//.: number of fatal health effects.
 h: subscript for heat energy.
 /„: initial inventory of radionuclide.
  /': subscript for radionuclide.
 k: permeability of porous medium.
 L: distance from disposal site to wellpoint.
  1: subscript for organs.
M: total number of organs considered.
Nd:
 n:
 P:
P':
 P-
 Q-

Q':

Q0:
Qw:
 R:
R/.
  r.
 T:
T.:
  t:
 td:
 U:
 u:
 V:
 v:
 x:
 z:
 d:
 r-
 d:
decay number ( = Xl/L/P/)-
porosity of porous medium.
Peclet number  (= VL/D).
population of community.
intensity of pressure.
rate of radionuclide transport with disperson
effect considered.
tate of radionuclide transport with dispersion
effect neglected.
rate of radionuclide transport at x =  0.
rate of groundwater flow.
rate of fluid withdrawal from the transport
system.
rate of heat loss of fluid.
retardation factor for porous medium.
risk conversion factor.
ratio of radioactivity being uptaken and that
reached the wellpoint.
temperature of fluid.
number of years of life expectancy.
time.
duration of radionuclide leaching.
internal energy.
unit response function with dispersion effects
being considered.
unit response function with dispersion effects
being neglected.
interstitial velocity of  groundwater.
velocity vector.
space coordinate in horizontal direction.
height above reference plane.
unit impulse function.
long-term  health effects conversion factor.
dimensionless time ( = rV/L).
viscosity of fluid.
radioactive decay constant.
radionuclide leaching factor.
instantaneous radionuclide transport correction
factor.
mass density of fluid.
dummy time variable.
                                                    B-12

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             APPENDIX C

RADE MODEL:   RADIOACTIVE  ATMOSPHERIC
    DISPERSION AND  EXPOSURE  CODE
            C-l

-------
                               INTRODUCTION


     The PRESTO-EPA  codeU)  for  calculating the environmental  transport  of
nuclides  from  low-level  waste   (LLW)  disposal  facilities,   includes   a
Gaussian Plume  model for  atmospheric transport.   However,  the code  only
allows for  the  calculation of one wind  sector,  speed, stability,  distance
and population  to  be specified for each  PRESTO-EPA  calculation.   In  order
to facilitate the determination of risk elements in the LLW  disposal  alter-
native  risk-cost  data  matrix,  a small  program called  RADE  (Radioactive
Atmospheric  ^Dispersion   and  Exposure)  has  been  written.   The  RADE  code
performs standard Gaussian PTume atmospheric dispersion  calculations  using
subroutines  from  PRESTO-EPA.    It   then   performs   the   Air-Pathway  Unit
Response analysis(2) and prepares  the output in the form  suitable for  input
to  PRESTO-EPA.   This  memorandum  documents  the RADE  code  and  its use  to
prepare input to PRESTO-EPA for the following settings:

     1)  Barnwell,  South Carolina

     2)  West Valley, New  York

     3)  Beatty, Nevada


                            METHOD OF ANALYSIS
     One  main  objective  in  developing  RADE  is   to   utilize  applicable
subroutines in PRESTO-EPA without altering them.  The MAIN  program collects
and  prints  out  the  necessary  input  data.    It  then  calls  the  AIRTRM
subroutine  for  the  analysis.    AIRTRM  in  turn   calls   several  support
subroutines.  The MAIN program then performs the unit response  analysis  and
outputs the parameters UEFF,  XG,  FTWIND, CHIQ and POP parameters  for input
into PRESTO.

     After the sector-independent data are read  in, RADE proceeds  through  a
DO  loop  in  which the sector-distance data  are input, AIRTRM is  called  and
the key data are accumulated.

     The RADE  code  is organized so that several wind speed  distributions,
stability  classes  or populations  within a  sector  can  be  included  in  the
analysis,  for  this  situation, the  data  for each  distribution  element  are
read in  as  a  new sector.   Thus,  for  example,  the sector designation para-
meter, ISEC, can  be  larger  than  16 even  though  only  16  compass sectors  are
used.   If  the  type  of  stability formation  or stability class varies with
the sector-distance  designations,  then the  original  source height,  read in
Card  2 must  be a  negative number.   The  source  height  for  each  sector-
distance designation  is read from input  card set 5B.

     The parameters  for the  community  designated as  the  PRESTO-EPA input
community must  be read  in  last.    A  complete  listing of  the  RADE  code is
given on pages  7-12 .


                                C-2

-------
                AIR CONCENTRATION AS A  FUNCTION  OF  DISTANCE
     In order to obtain  some insight into the impacts from  the  atmospheric
dispersion  pathway  for   large   populations   at  large  distances  from  the
facility, RADE2 was used to  calculate CHIQ values  as  a function  of  distance
for the  West  Valley meteorological  conditions.    The results are  shown  in
Figure  1  for  both  four  and three  atmospheric  stability  conditions.    At
large  distances both  curves  in  the  figure coincide  because  of  the  lid
height condition of 300 m used  in  the calculations.
                                  RESULTS
     The  air  pathway  unit response  calculations for  the  three reference
sites are summarized  below.   The complete RADE output,  including the  input
data for these sites  is given  in Appendix  B.
     Site            FTWIND

BarDwell, SC         0.080

West Valley, NY      0.288

Beatty, NV           6.025
 POP

  111

4,285

   50
CHIQ (sec/m3)

  1.20E-04

  3.25E-07

  5.23E-08
When  performing  the  PRESTO  calculations  the  CHIQ  is  read  in  so  that
subroutine AIRTRM is not called.
                                   c-3

-------
   10
X
Q
   10
   10-7-
      100
103               104
    DISTANCE (m)
       FIGURE 1.  CHIQ AS A  FUNCTION OF DISTANCE

                              C-4
 105

RAE-100811

-------
                    FIGURE 1.  CHIQ AS A FUNCTION OF DISTANCE
                                                        RAE-100811
X
6
   10 °-
   10-7-
      100
103                104
    DISTANCE (m)     c~5

-------
                           INPUT SPECIFICATIONS
     The input format for RADE is given below:
             Card No.      Format          Parameters

                                           Title Card
                                           H, VG, VD, HLID, ROUGH
                                           CHIQ, RE1, RE2, RES, RR, FTMECH
                                           IT, IS, ISEC
                                           XNAME(J), J = 1,4
                                           H, XG, U, FTWIND, POP

     Cards 5A and 5B are repeated for every sector-distance combination
being analyzed.

     A description of the input variables is given below.
1
2
3
4
5A
5B
20A4
8F10.0
8F10.0
815
4A4
8F10.0
              Variable

               H
               VG
               HLID
               ROUGH
               CHIQ
               RE1

               RE2

               RES

               RR
               FTMECH

               IT
               IS
               ISEC
               XNAME
               XG

               U

               FTWIND

               POP
            Description

Source height (m)
Velocity, gravitational fall (m/s)
Lid height (m)
Roughness parameter
1.0
Beginning coefficient in resuspension
equation (not used)
Decay factor in resuspension equation
(not used)
Final coefficient in resuspension equation
(not used)
(not used)
Fraction of year mechanical disturbance
occurs (not used)
Type of stability formulation
1 for PG
2 for Briggs-Smith
Stability class
Number of sector-distance combinations
Community name
Distance to the population  in the sector
of interest (m)
Windspeed in the sector of  interest
m/s)
Fraction of time the wind blows toward-
the sector of interest
Population at the sector-distance of
interest
                                       C-6

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                             RADE CODES

C     RADE
C     RADIOACTIVE ATMOSPHERIC DISPERSION AND EXPOSURE.
C     INCORPORATES AIRTRM AND RELATED SUBROUTINES FROH  PRESTO-EPA.
      PROGRAM RADE
      COMMON/AIR/H,VG,U fIT.IS,VD,XG.HLID,ROUGH.FTUIND,CHIQ,RE1,RE2,RE3
      DIMENSION A(20),XNAME(4)
      CALL ASSIGNS,'LA:')
      URITE(6,1000)
      READ(5,6000) (A(I),1=1.20)
      URITE(G,6010)  (A(I),I=i.20)
      Tl=0.
      T2=0.
      READ(5,3005) HH.VG,VD.HLID,ROUGH
      READ(5,3005) CHI3,RE1,RE2,RE3rRR,FTMECK
      READ(5,3010) IT,IS,ISEC
      WRITE(G,G400)
      WRITECG,G416)  ISEC
      IF (HH.GE.O.)  URITE(fa,6405)  HH
      WRITE(6.G410)  VG
      WRITE(6,6420)  VD
      URITE(b.6435)  HLID
      WRITE(6,6440)  ROUGH
      U8ITE(6,6445)  IT.IS
      URITE(6.6480)  REi,RE2,RE3
      URITE(6.6500)
      DO 1 1=1,ISEC
      READ(5,6000) (XNAME(J),J=1,4)
      READ(5,3005) XG.U.FTUIND,POP
      IFCHH.LT.O.) REAEK5.3010) IT.IS
      IFCHH.LT.O.) READ(5,3005) H,VG,VD,HLID.ROUGH
      IF(HH.GE.O-) H=HH
C
      CALL AIRTRM(EXPOS,DE?0!
r
      TO=EXPOSAPOP*FTUIND
      T1=T1+TO
      T2=T2+POF
      WRITE(6.5510)  (XNAME(J),J=l.4).XG.U.FTUIND,POP,EXPOS
    1 CONTINUE
      FTUIND=T1/(PGPAEXPOS)
      pT;-)T-T-,
      wE!TE(&,5520/
      USITE(G.b530)  (XNAriEC) ,J=1,4;, XG.U.FTWIND.PDF , EXPOS
      WRITE(6,£.540)  PTOT
 IOCC ;jR^AT'://.lBX.55r^'!./.i8X. r ,53X. ''A' ,/. 1SX. A'.23X.'S A D E .
                                  C-7

-------
     S'JSX,'A',/,1SX,'*',53X,'A',/,18X,'A',4X,'RADIOACTIVE ATMOSPHERIC DI
     ISPERSION X EXPOSURE',4Xf'A'./,18X,'A'.53X,'AV»13X»55('A'»
 3005 FORMAT(8F12.6)
 3010 FORMAK8I6)
 6000 FORMAT(20A4)
 6010 FORMAT(///,1X,20A4,///)
 6400 FORMAT(//,20X,'GENERAL  INPUT  DATA')
 6405 EORMAK//.11X, 'SOURCE  HEIGHT  IS  ',FG.l,'  METERS')
 6410 FORMATdlX,'VELOCITY OF GRAVITATIONAL FALL IS',FG.2,
     & '  METERS/SECOND')
 6416 FORMATU1X/NO.  OF  SECTOR  DISTANCE  COMBINATIONS IS', 14,/, 11X.
     X 'ENTER PRESTO  REFERENCE POPULATION  DATA  LAST')
 6420 FQRMATU1X,'DEPOSITION  VELOCITY  IS  ',F6.2,'  METERS/SECOND')
 6435 FORMAT(11X,'LID HEIGHT  IS  ',F8.2,'  METERS')
 6440 FORMATU1X/HOSKER  ROUGHNESS  FACTOR  IS ',F6.2)
 6445 FORMAT(11X,'TYFE OF STABILITY FORMULATION IS ',I2,/,
     & 11X.'STABILITY CLASS  IS  ',12)
 6480 FORMAT(11X,'RESUSPENSION FACTOR  PARAMETERS ',3(4X,1PE12.4))
 6500 FORMAT'///,3X,'COMMUNITY NAME',7X,'XG',3X,'WIND VELOCITY',4X,
     S 'FTWIND',6Xr'POP',llX.'CHIQ',/.24X,'(M)',10X.'(M/SEC>'r26X.
     I 'CI/MAA3 PER CI/SEC',/.90('-'),/)
 6510 FORMAT(2X,4A4f4XfF7.1,8X,E6.2f8X,F7.5,lXrF8.0,7X,lPE10.3)
 6520 FORMAT
      END
C
C
r
L<
      BLOCK DATA
      COMMON/C/BY(6).BZl(6)rBZ2(6),BZ3(6).Al(6),A2(6)?BK6),B2(6),
     SB3(6)fPY(6,5).PZ(6,5),QY(6r5)rOZ(6,5).XM(50)
      DATA BY/.22,.16,.11,.08,.06,.04/.
     &    BZ1/.2,.12,.08,.06,.03..016/,
     t    BZ2/0.,0.,.0002,.0015,.0003,.0003/,
     &    BZ3/l.,l.,-.5,-.5,-l..-l./
      DATA Al/-.0234.-.0147,-.0117.-.0059,-.0059,-.0029/,
     S     A2/.35f.248,.175,.108..6B8,.054/,
     S     Bl/.86,-.985,-1.186,-1.35,-2.88,-3.8/,
     S     B2/-.152,.82,.85,.793,1.255,1.4197,
     I     B37.1475,.0168,.0045,.0022,-.042,-.0557
      DATA PY/.469,.306,.23..219..237..237,0.,.4..36,.32,0.,.31,
     I        0..1.7,1.44,.91,1.02,0...66..66,.63,.53,.41,7.56,
     S        .34,.37..40,.43,.46,7.567
      DATA QY/.903..885..855,.764,.691,.594,0.,.91,.36,.78,0...71,
     S        0.T. 717. .71, .729, .648,0. ..S3. .83, ,50, .8!)'.. 87, .52.
     8,        1.00,.94,.S8,.82,.7&,i.527
      DATA PZ/.017,.072..07&,.14,.217,.262,0.,.411,.326,.223.0.,
     I        .062.0...079..131..91.1.93.0.,.14..14,.21..26,. 13..56,
     S        .037,.076,.I6..32,nfa6.1.37/
                                  C-8

-------
      LifilA U2/1.38,1.021,.879,.727,.61,.5,0.,.907,.859..776,0.,.709,
     8        0.,1.2,1.046,.702,.465,0.,1.09,1.09,.98,.89,.83,.55,1.28,
     &        1.12..96,.88,.63,.477
      DATA XM/1.00.2.00,3.00,4.00,5.00,10.0.15.0,20.0,25.0,30.0,
     8        35.0,40.0,45.0,50.0,150.,200.,300.,400.,500.,600.,
     I        70Q.,800.,900.,1.E3,1.1E3.1.2E3,1.3E3,1.4E3,1.6E3,1.8E3,
     S        2.0E3,2.5E3,3.0E3,3.5E3,4.0E3,4.5E3,5.0E3,6.E3,7.E3,8.E3,
     S        1.0E4,1.5E4,2.E4.3.E4,4.E4,5.E4.6.E4,7.E4,8.E4,1.E5/
      END
C
C
C
      SUBROUTINE AIRTRM(EXPOS,DEPQ)
      COMMON/AIF/H,VQ,U,IT,IS,VD.XG,HLID,ROUQH,FTWIND,CHIQ.SE1,RE2,RE3
      IF(IS.LT.1.0R.I8.GT.6) WRITE(6r38) IT,IS
      IF(IT.EQ.5.AND.(IS.EQ.1.0R.IS.EQ.5» WRITE(6,38) IT,IS
      IF(IT.EQ.6.AND.(IS.EQ.1.0R.IS.EQ.6)) URITE(6,38) IT,IS
   38 FORMAK2X,'INVALID COMBINATION OF IT=',I2,' AND IS=',I2>
      PI=3.141593
      IFtHLID.EQ.O.) HLID=12000.
      LID=HLID
      HH=H-VGAXG/U
      IF(HH.LT.O.) HH=0.
C
      CALL SIGMAZ(XG. IT, IS,ROUGH„SIGZ,IKPM,HLID,VG,U,HH)
C
      CQR=1.
      IF(VG.EQ.O.O.AND.yn.EQ.O.) GO TO 45
C
      CALL DPLT(FI,HH,VD,U,IT,!S,XG,ROUGH,HLID,COR,VG,H>
C
   45 EXPO=EXP(-0.5AHHAHH/(SIGZASIGZ >)
      EXPN=CORA2.032*EXPO/(SIGZAXG)
      EXPOS=EXPN/U
      DEPO=EXPOSAVD
   80 CONTINUE
      RETURN
      END
C
C
C
      SUBROUTINE DPLTCPI.HH,VD,U.IT,ISfXQ,RQUGH,HLIDfCOR,VQ.H)
      DIMENSION XX(50)rEX(50),AX(50)
      COMMON/C/BY(6;.BZl(6),BZ2(fa),BZ3(6),Al(6).A2(6).BK6),B2(b),
     &B3(b>fPY(b.5),PZ(G.5),QY(6,5J,GZ(6.5),Xh(50)
      IEdS.GT.6) IS=6
      IKPH-1
      IDUM=1
f
L/
      C ALL S Ii3MAZ (XG. II, IS, ROUGH, 3 IGZ, IKPM, HL ID, VG, U, HH )
                                C-9

-------
      IKPM=IKPH+1
      SQRTP1=0.79785
      FX (IKP) =EXP (-0. 5AHHAHH/ (SIGZASIGZ)) ,'S IGZ
      XX(IKP)=XG
      DO 20 I=1,IKPM
      XX(I)=XM(I)
C
      CALL SIGMAZ(XX(I),IT.IS,ROUGH,SIGZ,IDUM,HLID,VG.U,HH)
C
      FX(I)=EXP(-0.5AHHAHH/(SIGZASIGZ))/SIGZ
   20 CONTINUE
      L=l
C
      CALL SIMPUN(XX,FX,IKP,L.AX)
C
      COR=EXP(-SQRTPIAVDAAX(IKP)/U)
      RETURN
      END
C
C
C
      SUBROUIINE SIGMAZ(XG,IT,IS.ROUGH,SIGZ,IKPM,HLID,VG,U,HH)
      COMMON/'C/BY(6),BZ1(&),BZ2(&),BZ3(G>,A1(&),A2(&),B1(GJ,B2(6>,
     &B3(&),PY(&,5),PZ(&,5),QY(6,5J,QZ(6,5),Xh(50)
      DIMENSION AONE(&),BONE(6),ATUO(&>fBTWO(fa),CONE(6).DONE(G),
     8CTUO(G),DTUOCG)JW3H(6)
      DATA AONE/0.112,0.130,0.112,0.098,0.0609,O.OG38/
      DATA BONE/1.06,0.950,0.920,0.889,0.895,0.783/
      DATA ATUO/5.38E-4,6.52E-4,9.05E-4,1.35E-3.1.9&E-3.1.36E-3/
      DATA BTUO/0.815,0.750,0.718,0.688,0.684,0.672/
      DATA CONE/1.56,2.02,2.72,5.16,7.37,11.7/
      DATA DONE/0.0480,0.0269,6.,-0.060,-0.0957,-0.128/
      DATA CTUO/6.25E-4.7.76E-4,0..186..4290..45900./
      DATA DIUO/0.45,0.37,0.,-0.225,-0.60,-0.78/
      DATA RGH/0.01,0.04,0.10.0.40,1.0,4.O/
      P=0n
      BO 8 1=1,50
      IKP=I
      IF(XHd).GE.XG)  GO  TO  9
    8 CONTINUE
    9 IECIKP.LT.2)  IKP=2
      IKPM=IKP-1
      IPOINT=IT
      IFCIT.GT.3} IPOINI=4
      GO TO (10,20,30,40) IPO INT
   10 ALX=ALOG(XG)
      SIGZ=EXP(B1(IS)+(B2(IS)+B3(IS)AALX)AALX)/:.15
      ^Q jn go
   20 ABS=ROUGH
      CI^YLAG(ABB.RGH.CONE.0.3,6,0)
      D1=YLAGCAB3.RGH,DONE.G,2.£,05
                               C-10

-------
      Uii= I Lftij (. fltfb , KljH , LIWU , 0 , 'J , b , 0 )
      D2=YLAG(ABS,RGH,DTUOrO,2,6,0>
      G=AONE( IS)AXGAABONE< IS)/(1.+ATUO( IS)AXGAABTUO( IS) )
      F=ALOG(F)
      IFCROUGH.LE.0.10) GO TO 26
      F=F+ALOG ( 1 . +1 ./(C2AXGAAD2) )
      GO TO 27
   26 E=F-ALQG<1.+C2AXGAAD2)
   27 SIGZ=GAF
      IF(SIGZ.LI.l.) SIGZ=1.
      GO TO 99
   30 SIGZ=BZ1
      GO TO 99
   40 2=11-3
      SIGZ=PZ(IS,J)AXGAAQZ(IS,J)
   99 SIGCAL=2.A(HLID-0.5AHH)/2.15
      IF(SIGZ.LT.SIGCAL) GO TO 1000
      SIGZ=SIGCAL
 1000 RETURN
      END
r
w
C
c
      SUBROUTINE SIMPUN(XX,FX,NX, I,AX>
      DIMENSION XX(2),FX(2).AX(2)
      IF(I.LT.O) GO TO 30
      AX(1)=0.
      DO 10 IX=2,NX,2
      D1=XX(IX)-XX(IX-1)
      AX(IX)=AX(IX-1)+0.5AD1A(FX(IX)+FX(IX-D)
      IF(NX.EQ.IX) GO TO 20
      D2=XX(IX+1)-XX(IX-1>
      D3=D2/D1
      A2=D3/6 - AD2AD2/ ( XX ( IX+ 1 5 -XX ( IX ) )
      A3=0.5AD2-A2/D3
   10 AX(IX+1)=AX(IX-1)+(D2-A2-A3)AFX(IX-1)+A2AEX(IX)+A3AFX(IX+1)
   20 RETURN
   30 AX(NX)=0.
      DO 40 IX=2,NX,2
      IC=NX+1-IX
      D1=XX(IC+1)-XX(IC)
      AX(IC)=AX(IC+1)+0.5AD1*(FX(IC+1)+EX(IC))
      IF(NX.EQ.IX) GO TO 20
      D2=XX(IC+1)-XX(IC-1)
      D3=D2/(XX(IC)-XX(IC-D)
      A2=D3AD2AD2/(6.AD1)
      A3=0.5AD2-A2/D3
   40 AX(IC-l)=AX(IC+l) + aC-A2-A3)AFX(IC-l)+A2AFX(IC)+A3AFX(IC-^l)
      RETURN
      END
                               C-ll

-------
c
c
c
      FUNCTION YLAG(XI.X,Y,IND1,N1,IMAX,IEX)
      DIMENSION X(1),Y<1)
      IND=IND1
      N=N1
      IEX=0
      IF(N.LE.IMAX)  GO TO 10
      N=IHAX
      IEX=N
   10 IF(IND.GT.O) GO TO 40
      HO 20 J=lrIMAX
      IF(XI-X(J)) 30,130,20
   20 CONTINUE
      IEX=1
      GO TO 70
   30 IND=J
   40 IF(IND.GT.l) GO TO 50
      IEX=-1
   50 INL=IND-(N+l)/2
      IF(INL.GT.O) GO TO 60
      INL=1
   60 INU=INL+N-1
      IF(INU.LE.IMAX) GO TO  80
   70 INL=IMAX-N+1
      :NU=IMAX
   80 5=0.
      p=l.
      no no J=INL,INU
      P=FA(XI-X(J))
      D=l.
      HO 100 I=INL.INU
      IF(I.NE.J) GO TO 90
      XD=XI
      GO TO 100
   90 XD=X(J)
  100 D=DA(XD-X(D)
  110 S=S+Y(J)/D
      YLAG^SAP
  120 RETURN
  130 YLAG=Y(J)
      GO TC 120
      END
                                C-12

-------
                 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
                 A
                 A
                 A
                 A
                 A
                    R A D E
 RADIOACTIVE ATMOSPHERIC DISPERSION 2 EXPOSURE
                                 A
                                 A
                                 A
                                 A
                                 A
                 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
    B E A T T Y
                   GENERAL INPUT DATA
          NO.  OF SECTOR DISTANCE COMBINATIONS IS   6
          ENTER PRESTO REFERENCE POPULATION DATA LAST
          SOURCE HEIGHT IS    1.0 METERS
          VELOCITY OF GRAVITATIONAL FALL IS  0.03 METERS/SECOND
          DEPOSITION VELOCITY IS   0.03 METERS/SECOND
          LID HEIGHT IS   300.00 METERS
          HOSKER ROUGHNESS FACTOR IS   0.01
          TYPE OF STABILITY FORMULATION IS  1
          STABILITY CLASS IS  4
          RESUSPENSION FACTOR PARAMETERS       l.OOOOE-04      -1.5000E-01
                                                         l.OOOOE-09
COMMUNITY NAME
BEATTY
DEATH VALLEY
DEATH VALLEY JN.
LATHROY WELLS
PAHRUMP
FARM VILLAGE
XG
CM)
17000.0
40000.0
58000.0
29000.0
87000.0
29000.0
WIND VELOCITY
(M/SEC)
4.80
4.80
4. SO
4.80
4.80
4.80
FTWIND
0.09000
0.17000
0.11000
0.25000
0.25000
0.25000
POP CHIQ
CI/MAA3 PER C I/SEC
900.
25.
30.
250.
1000.
50.
S.923E-08
3.792E-08
2.615E-G8
5.231E-08
1.744E-08
5.231E-08
	  PRESTO INPUT

 FARM VILLAGE
29000.0
4.30
6.02439
5.231E-OS
        AIR PATHWAY POPULATION IS
                                        C-13

-------
                AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
                A
                A
                A
                A
                A
                             R A D E
          RADIOACTIVE ATMOSPHERIC DISPERSION X EXPOSURE
                   A
                   A
                   A
                   A
                   A
                AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
    BARNUELL
                   GENERAL  INPUT  DATA
          NO.  OF  SECTOR  DISTANCE  COMBINATIONS  IS    7
          ENTER PRESTO REFERENCE  POPULATION  DATA  LAST
          SOURCE HEIGHT IS    1.0  METERS
          VELOCITY OF GRAVITATIONAL FALL IS  0.10  METERS/SECOND
          DEPOSITION VELOCITY  IS   0.10 METERS/SECOND
          LID HEIGHT IS   300.00 METERS
          HOSKER ROUGHNESS FACTOR  IS   0.01
          TYPE OF STABILITY FORMULATION IS  1
          STABILITY CLASS IS  4
          RESUSPENSION FACTOR  PARAMETERS       l.OOOOE-06     -1.5000E-01
                                                                   l.OOOOE-11
COMMUNITY NAME
BARNUELL CITY
BLACKVILLE
UILLISTON
ELKO
HILDA
KLINE
3NELLING
XG
(M)
8050.0
21900.0
1S200.0
16400.0
20300.0
16700.0
480.0
WIND VELOCITY
(M/SEC)
2.01
2.01
2.01
2.01
2.01
2. ,01
2.01
FTUIND
0.09000
0.05000
0.02000
0.03000
0.06000
0.05000
0.05000
POP
5572.
2840.
3173.
qoq
!_' XJ -• »
ncrrr
OlJvJ B
3i D B
in.
CHIO
CI/MAA3 PER C I/SEC
S.968E-07
1.654E-Q7
1.990E-07
2.209E-07
1 ^C^T fW
1 • / u %J C V i
2.169E-07
1.20IE-04
	 PRESTO INPUT

 SMELLING
           480.0
,07962
                                                              111,
  « n *" ?• i-
  i L' i H L
PATHWAY POPULATION IS   12695.
                                         C-14

-------
                AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
                A                                                     A
                A                       R A D E                       A
                A                                                     A
                A    RADIOACTIVE ATMOSPHERIC DISPERSION I EXPOSURE    A
                *                                                     A
                AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
   WEST
VALLEY
                  GENERAL INPUT DATA
         NO. OF SECTOR DISTANCE COMBINATIONS IS  33
         ENTER PRESTO REFERENCE POPULATION DATA LAST
         SOURCE HEIGHT  IS    1.0 METERS
         VELOCITY OF GRAVITATIONAL FALL IS  0.01 METERS/SECOND
         DEPOSITION VELOCITY IS   0.01 METERS/SECOND
         LID HEIGHT IS   300.00 METERS
         HOSKER ROUGHNESS FACTOR IS   0.01
         TYPE OF STABILITY FORMULATION
         STABILITY CLASS  IS  4
         RESUSPENSION FACTOR PARAMETERS
                         IS  1
                                l.OOOOE-06
                        -1.5000E-01
     l.OOOOE-10
COMMUNITY NAME
XG
(M)
WIND VELOCITY
(M/SEC)
FTWIND
POP
CHIQ
CI/MAA3 PER C I/SEC
GLENUOOD
CHAFFEE
PROTECTION
SANDUSKY
ELTON
FARMERSVILLE
HUMPHREY C.
HUMPHREY
      19300.0
      19300.0
      21700.0
      22500.0
      17700.0
      23300.0
      25700.0
      2R200.0
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
0.07170
0.08670
0.08670
0.06380
0.10650
0.09370
0.04860
100
100
100
500
50
978
20
7.545E-OS
7.545E-08
6."HE-OS
6.472E-08
S.227E-08
6.250E-OS
5.666E-08
                                         C-15

-------
SUGARTOWN
GREAT VALLEY
MARSHFIELD
LANGFORD
NEW OREGON
BOSTON
GOLDEN
GOUANDA
CATTARANGUS
ELLICQTTVILLE
ARCADE
ERANKLINVILLE
RICEVILLE
WEST VALLEY
ASHFORD VALLEY
EAST CONCORD
SARDINIA
YORKSHIRE
LIHE LAKE
h'ACHIAS
ASHFORD
EAST OTTO
OTTO
COLLINS CENTER
SPRINGY ILLE
23300.0
25700.0
19300.0
22500.0
19300.0
20900.0
21700.0
23300.0
21700.0
19300.0
20900.0
20100.0
2400.0
5630.0
5630.0
11300.0
15300.0
17200.0
14500.0
12900.0
14500.0
11300.0
18500.0
17700.0
7420.0
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5.00
5. .00
0.04270
0.04270
0.08890
0.08890
0.08890
0.06490
0.07170
0.02500
0.01320
0.04270
0.08670
0.06530
0.09370
0.04860
0.01320
0.04270
0.08670
0.08670
0.10650
0.06380
0.04270
0.01320
0.01320
0-04990
0.07170
150.
2014.
100.
100.
100.
7687.
3128.
2712..
1200.
1677.
3714.
3102.
30.
600.
100.
8171.
2792.
3620.
1191.
2058.
1922.
942.
828.
5037.
4285.
6.250E-08
5.666E-08
7.545E-06
6.472E-03
7.545E-08
6.968E-08
6.711E-08
6.250E-08
6.711E-08
7.545E-08
6.968E-08
7.245E-08
2.565E-06
5.392E-07
5.392E-07
1.504E-07
9.518E-08
8.467E-08
1.004E-07
1.180E-07
1.004E-07
1.504E-07
7.S72E-OS
S.227E-08
3.252E-07
	  PRESTO  INPUT




 SPRINGVILLE
7420.0
5.00
0.28829
  TOTAL  AIR  PATHWAY  POPULATION  IS    59638.
                                         C-16

-------
                                 REFERENCES
1.  C. Little,  et  al.,  "PRESTO-EPA:  A  Low-Level  Radioactive Waste
    Environmental  Transport and Risk Assessment Code—Methodology and
    User's Manual,"  EPA Report (in print).

2.  C.Y. Hung,  et  al.,  "Use of PRESTO-EPA  Model in Assessing Health Effects
    From Land  Disposal  of LLW to Support EPA's Environmental Standards,"
    Presented  at the 5th Annual DOE LLW participants Information Meeting,
    Denver,  Colorado, August 30 - September  1, 1983.
                                     *U.S. Government Printing Office
                                                            1988  516-002/80061
                                 C-17

-------